Primitivele funcțiilor logaritmice

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Disponibil în 32 limbi" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-32" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">32 limbi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Lys_van_integrale_van_logaritmiese_funksies" title="Lys van integrale van logaritmiese funksies – afrikaans" lang="af" hreflang="af" data-title="Lys van integrale van logaritmiese funksies" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%AA%D9%83%D8%A7%D9%85%D9%84%D8%A7%D8%AA_%D8%A7%D9%84%D8%AF%D9%88%D8%A7%D9%84_%D8%A7%D9%84%D9%84%D9%88%D8%BA%D8%A7%D8%B1%D9%8A%D8%AA%D9%85%D9%8A%D8%A9" title="قائمة تكاملات الدوال اللوغاريتمية – arabă" lang="ar" hreflang="ar" data-title="قائمة تكاملات الدوال اللوغاريتمية" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B0%D0%B1%D0%BB%D0%B8%D1%86%D0%B0_%D1%81_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%B8_%D0%BD%D0%B0_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%BC%D0%B8%D1%87%D0%BD%D0%B8_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8" title="Таблица с интеграли на логаритмични функции – bulgară" lang="bg" hreflang="bg" data-title="Таблица с интеграли на логаритмични функции" data-language-autonym="Български" data-language-local-name="bulgară" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A6%97%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B0%E0%A6%BF%E0%A6%A6%E0%A6%AE%E0%A6%BF%E0%A6%95_%E0%A6%85%E0%A6%AA%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%95%E0%A7%87%E0%A6%B0_%E0%A6%B8%E0%A6%AE%E0%A6%BE%E0%A6%95%E0%A6%B2%E0%A7%87%E0%A6%B0_%E0%A6%A4%E0%A6%BE%E0%A6%B2%E0%A6%BF%E0%A6%95%E0%A6%BE" title="লগ্যারিদমিক অপেক্ষকের সমাকলের তালিকা – bengaleză" lang="bn" hreflang="bn" data-title="লগ্যারিদমিক অপেক্ষকের সমাকলের তালিকা" data-language-autonym="বাংলা" data-language-local-name="bengaleză" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Spisak_integrala_logaritamskih_funkcija" title="Spisak integrala logaritamskih funkcija – bosniacă" lang="bs" hreflang="bs" data-title="Spisak integrala logaritamskih funkcija" data-language-autonym="Bosanski" data-language-local-name="bosniacă" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Llista_d%27integrals_de_funcions_logar%C3%ADtmiques" title="Llista d'integrals de funcions logarítmiques – catalană" lang="ca" hreflang="ca" data-title="Llista d'integrals de funcions logarítmiques" data-language-autonym="Català" data-language-local-name="catalană" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Seznam_integr%C3%A1l%C5%AF_logaritmick%C3%BDch_funkc%C3%AD" title="Seznam integrálů logaritmických funkcí – cehă" lang="cs" hreflang="cs" data-title="Seznam integrálů logaritmických funkcí" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%BB%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%81%D0%B5%D0%BD_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%C4%95%D1%81%D0%B5%D0%BD_%D0%B9%D1%8B%D1%88%C4%95" title="Логарифмла функцисен интегралĕсен йышĕ – ciuvașă" lang="cv" hreflang="cv" data-title="Логарифмла функцисен интегралĕсен йышĕ" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/List_of_integrals_of_logarithmic_functions" title="List of integrals of logarithmic functions – engleză" lang="en" hreflang="en" data-title="List of integrals of logarithmic functions" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Listo_de_integraloj_de_logaritmaj_funkcioj" title="Listo de integraloj de logaritmaj funkcioj – esperanto" lang="eo" hreflang="eo" data-title="Listo de integraloj de logaritmaj funkcioj" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zerrenda:Funtzio_logaritmikoen_integralak" title="Zerrenda:Funtzio logaritmikoen integralak – bască" lang="eu" hreflang="eu" data-title="Zerrenda:Funtzio logaritmikoen integralak" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D9%87%D8%B1%D8%B3%D8%AA_%D8%A7%D9%86%D8%AA%DA%AF%D8%B1%D8%A7%D9%84%E2%80%8C%D9%87%D8%A7%DB%8C_%D8%AA%D9%88%D8%A7%D8%A8%D8%B9_%D9%84%DA%AF%D8%A7%D8%B1%DB%8C%D8%AA%D9%85%DB%8C" title="فهرست انتگرال‌های توابع لگاریتمی – persană" lang="fa" hreflang="fa" data-title="فهرست انتگرال‌های توابع لگاریتمی" data-language-autonym="فارسی" data-language-local-name="persană" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Primitives_de_fonctions_logarithmes" title="Primitives de fonctions logarithmes – franceză" lang="fr" hreflang="fr" data-title="Primitives de fonctions logarithmes" data-language-autonym="Français" data-language-local-name="franceză" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Popis_integrala_logaritamskih_funkcija" title="Popis integrala logaritamskih funkcija – croată" lang="hr" hreflang="hr" data-title="Popis integrala logaritamskih funkcija" data-language-autonym="Hrvatski" data-language-local-name="croată" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%B8%D5%A3%D5%A1%D6%80%D5%AB%D5%A9%D5%B4%D5%A1%D5%AF%D5%A1%D5%B6_%D6%86%D5%B8%D6%82%D5%B6%D5%AF%D6%81%D5%AB%D5%A1%D5%B6%D5%A5%D6%80%D5%AB_%D5%AB%D5%B6%D5%BF%D5%A5%D5%A3%D6%80%D5%A1%D5%AC%D5%B6%D5%A5%D6%80%D5%AB_%D6%81%D5%A1%D5%B6%D5%AF" title="Լոգարիթմական ֆունկցիաների ինտեգրալների ցանկ – armeană" lang="hy" hreflang="hy" data-title="Լոգարիթմական ֆունկցիաների ինտեգրալների ցանկ" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Daftar_integral_dari_fungsi_logaritmik" title="Daftar integral dari fungsi logaritmik – indoneziană" lang="id" hreflang="id" data-title="Daftar integral dari fungsi logaritmik" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Tavola_degli_integrali_indefiniti_di_funzioni_logaritmiche" title="Tavola degli integrali indefiniti di funzioni logaritmiche – italiană" lang="it" hreflang="it" data-title="Tavola degli integrali indefiniti di funzioni logaritmiche" data-language-autonym="Italiano" data-language-local-name="italiană" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%AF%BE%E6%95%B0%E9%96%A2%E6%95%B0%E3%81%AE%E5%8E%9F%E5%A7%8B%E9%96%A2%E6%95%B0%E3%81%AE%E4%B8%80%E8%A6%A7" title="対数関数の原始関数の一覧 – japoneză" lang="ja" hreflang="ja" data-title="対数関数の原始関数の一覧" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%8F%E1%9E%B6%E1%9E%9A%E1%9E%B6%E1%9E%84%E1%9E%A2%E1%9E%B6%E1%9F%86%E1%9E%84%E1%9E%8F%E1%9F%81%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9B%E1%9E%93%E1%9F%83%E1%9E%A2%E1%9E%93%E1%9E%BB%E1%9E%82%E1%9E%98%E1%9E%93%E1%9F%8D%E1%9E%9B%E1%9F%84%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%B8%E1%9E%8F" title="តារាងអាំងតេក្រាលនៃអនុគមន៍លោការីត – khmeră" lang="km" hreflang="km" data-title="តារាងអាំងតេក្រាលនៃអនុគមន៍លោការីត" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmeră" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%A1%9C%EA%B7%B8%ED%95%A8%EC%88%98_%EC%A0%81%EB%B6%84%ED%91%9C" title="로그함수 적분표 – coreeană" lang="ko" hreflang="ko" data-title="로그함수 적분표" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BD%D0%B0_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%B8_%D0%BD%D0%B0_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC%D1%81%D0%BA%D0%B8_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B8" title="Список на интеграли на логаритамски функции – macedoneană" lang="mk" hreflang="mk" data-title="Список на интеграли на логаритамски функции" data-language-autonym="Македонски" data-language-local-name="macedoneană" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Lijst_van_integralen_van_logaritmische_functies" title="Lijst van integralen van logaritmische functies – neerlandeză" lang="nl" hreflang="nl" data-title="Lijst van integralen van logaritmische functies" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Lista_de_integrais_de_fun%C3%A7%C3%B5es_logar%C3%ADtmicas" title="Lista de integrais de funções logarítmicas – portugheză" lang="pt" hreflang="pt" data-title="Lista de integrais de funções logarítmicas" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%BE%D0%B2_%D0%BE%D1%82_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%84%D0%BC%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D1%85_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B9" title="Список интегралов от логарифмических функций – rusă" lang="ru" hreflang="ru" data-title="Список интегралов от логарифмических функций" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Lista_integrala_logaritamskih_funkcija" title="Lista integrala logaritamskih funkcija – sârbo-croată" lang="sh" hreflang="sh" data-title="Lista integrala logaritamskih funkcija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="sârbo-croată" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Seznam_integralov_logaritemskih_funkcij" title="Seznam integralov logaritemskih funkcij – slovenă" lang="sl" hreflang="sl" data-title="Seznam integralov logaritemskih funkcij" data-language-autonym="Slovenščina" data-language-local-name="slovenă" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Lista_e_integraleve_t%C3%AB_funksioneve_logaritmike" title="Lista e integraleve të funksioneve logaritmike – albaneză" lang="sq" hreflang="sq" data-title="Lista e integraleve të funksioneve logaritmike" data-language-autonym="Shqip" data-language-local-name="albaneză" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%B0%D0%BA_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%B0_%D0%BB%D0%BE%D0%B3%D0%B0%D1%80%D0%B8%D1%82%D0%B0%D0%BC%D1%81%D0%BA%D0%B8%D1%85_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" title="Списак интеграла логаритамских функција – sârbă" lang="sr" hreflang="sr" data-title="Списак интеграла логаритамских функција" data-language-autonym="Српски / srpski" data-language-local-name="sârbă" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%9F%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AF%88%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AF%81%E0%AE%95%E0%AE%B3%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%88%E0%AE%AF%E0%AF%80%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AE%B3%E0%AE%BF%E0%AE%A9%E0%AF%8D_%E0%AE%AA%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De la Wikipedia, enciclopedia liberă</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><table cellpadding="3" cellspacing="0" style="float:right; margin:5px; border:3px solid;"> <tbody><tr> <td style="border-bottom:3px solid; background:#efefef;"><small> Acest articol face parte din seria de articole<br /><b><a href="/w/index.php?title=Liste_de_primitive&action=edit&redlink=1" class="new" title="Liste de primitive — pagină inexistentă">Primitive</a></b> ale diferitelor <b><a href="/wiki/Func%C8%9Bie" title="Funcție">funcții</a></b></small> </td></tr> <tr> <td><b><a href="/wiki/Tabel_de_integrale" title="Tabel de integrale">Tabel de integrale</a></b> </td></tr> <tr> <td><a href="/wiki/Primitivele_func%C8%9Biilor_ra%C8%9Bionale" title="Primitivele funcțiilor raționale">Raționale</a> </td></tr> <tr> <td><a class="mw-selflink selflink">Logaritmice</a> </td></tr> <tr> <td><a href="/wiki/Primitivele_func%C8%9Biilor_exponen%C8%9Biale" title="Primitivele funcțiilor exponențiale">Exponențiale</a> </td></tr> <tr> <td><a href="/wiki/Primitivele_func%C8%9Biilor_ira%C8%9Bionale" title="Primitivele funcțiilor iraționale">Iraționale</a> </td></tr> <tr> <td><a href="/wiki/Primitivele_func%C8%9Biilor_trigonometrice" title="Primitivele funcțiilor trigonometrice">Trigonometrice</a> </td></tr> <tr> <td><a href="/w/index.php?title=Primitivele_func%C8%9Biilor_hiperbolice&action=edit&redlink=1" class="new" title="Primitivele funcțiilor hiperbolice — pagină inexistentă">Hiperbolice</a> </td></tr> <tr> <td><a href="/w/index.php?title=Primitivele_func%C8%9Biilor_invers_trigonometrice&action=edit&redlink=1" class="new" title="Primitivele funcțiilor invers trigonometrice — pagină inexistentă">Invers trigonometrice</a> </td></tr> <tr> <td><a href="/w/index.php?title=Primitivele_func%C8%9Biilor_hiperbolice_reciproce&action=edit&redlink=1" class="new" title="Primitivele funcțiilor hiperbolice reciproce — pagină inexistentă">Hiperbolice reciproce</a> </td></tr></tbody></table> <p>Următorul articol este o listă de <a href="/wiki/Integral%C4%83" title="Integrală">integrale</a> (<a href="/wiki/Primitiv%C4%83_(matematic%C4%83)" class="mw-redirect" title="Primitivă (matematică)">primitive</a>) de <a href="/wiki/Logaritm" title="Logaritm">funcții logaritmice</a>. Pentru o listă cu mai multe integrale, vezi <a href="/wiki/Tabel_de_integrale" title="Tabel de integrale">tabel de integrale</a> și <a href="/w/index.php?title=Lista_integralelor&action=edit&redlink=1" class="new" title="Lista integralelor — pagină inexistentă">lista integralelor</a>. </p><p><i>Notă:</i> Se presupune <i>x</i>>0 . </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \ln cx\;dx=x\ln cx-x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mi>x</mi> <mo>−</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \ln cx\;dx=x\ln cx-x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ea98e0c7eecf01738da468995c70fbeccaffa00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.083ex; height:5.676ex;" alt="{\displaystyle \int \ln cx\;dx=x\ln cx-x}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \ln(ax+b)\;dx=x\ln(ax+b)-x+{\frac {b}{a}}\ln(ax+b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>b</mi> <mi>a</mi> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \ln(ax+b)\;dx=x\ln(ax+b)-x+{\frac {b}{a}}\ln(ax+b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c75dd09aa8217f55798f3a3c3e3de15bce433559" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.489ex; height:5.843ex;" alt="{\displaystyle \int \ln(ax+b)\;dx=x\ln(ax+b)-x+{\frac {b}{a}}\ln(ax+b)}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int (\ln x)^{2}\;dx=x(\ln x)^{2}-2x\ln x+2x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mn>2</mn> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int (\ln x)^{2}\;dx=x(\ln x)^{2}-2x\ln x+2x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/972ad1bc9ef59adfee7013e457529fed94329dad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:37.56ex; height:5.676ex;" alt="{\displaystyle \int (\ln x)^{2}\;dx=x(\ln x)^{2}-2x\ln x+2x}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int (\ln cx)^{n}\;dx=x(\ln cx)^{n}-n\int (\ln cx)^{n-1}dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>−</mo> <mi>n</mi> <mo>∫</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>c</mi> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int (\ln cx)^{n}\;dx=x(\ln cx)^{n}-n\int (\ln cx)^{n-1}dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc2e71f415a7da575472261d7c93bf65f43335ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.347ex; height:5.676ex;" alt="{\displaystyle \int (\ln cx)^{n}\;dx=x(\ln cx)^{n}-n\int (\ln cx)^{n-1}dx}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{\ln x}}=\ln |\ln x|+\ln x+\sum _{i=2}^{\infty }{\frac {(\ln x)^{i}}{i\cdot i!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> </mrow> <mrow> <mi>i</mi> <mo>⋅</mo> <mi>i</mi> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{\ln x}}=\ln |\ln x|+\ln x+\sum _{i=2}^{\infty }{\frac {(\ln x)^{i}}{i\cdot i!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c15df4866128a1f83aba508a61dd6a560edcbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:38.015ex; height:7.009ex;" alt="{\displaystyle \int {\frac {dx}{\ln x}}=\ln |\ln x|+\ln x+\sum _{i=2}^{\infty }{\frac {(\ln x)^{i}}{i\cdot i!}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{(\ln x)^{n}}}=-{\frac {x}{(n-1)(\ln x)^{n-1}}}+{\frac {1}{n-1}}\int {\frac {dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>n</mi> <mo>≠</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{(\ln x)^{n}}}=-{\frac {x}{(n-1)(\ln x)^{n-1}}}+{\frac {1}{n-1}}\int {\frac {dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3404d427d08ce2c31313b894105004b7075379b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:72.914ex; height:6.176ex;" alt="{\displaystyle \int {\frac {dx}{(\ln x)^{n}}}=-{\frac {x}{(n-1)(\ln x)^{n-1}}}+{\frac {1}{n-1}}\int {\frac {dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int x^{m}\ln x\;dx=x^{m+1}\left({\frac {\ln x}{m+1}}-{\frac {1}{(m+1)^{2}}}\right)\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>+</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>m</mi> <mo>≠</mo> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int x^{m}\ln x\;dx=x^{m+1}\left({\frac {\ln x}{m+1}}-{\frac {1}{(m+1)^{2}}}\right)\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/501bf3099de7ef237e7fb52a608a82d8058fed39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:66.552ex; height:6.343ex;" alt="{\displaystyle \int x^{m}\ln x\;dx=x^{m+1}\left({\frac {\ln x}{m+1}}-{\frac {1}{(m+1)^{2}}}\right)\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int x^{m}(\ln x)^{n}\;dx={\frac {x^{m+1}(\ln x)^{n}}{m+1}}-{\frac {n}{m+1}}\int x^{m}(\ln x)^{n-1}dx\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>m</mi> <mo>≠</mo> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int x^{m}(\ln x)^{n}\;dx={\frac {x^{m+1}(\ln x)^{n}}{m+1}}-{\frac {n}{m+1}}\int x^{m}(\ln x)^{n-1}dx\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4785399621a3b66973b823ab664772c00c28c66e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:80.077ex; height:6.343ex;" alt="{\displaystyle \int x^{m}(\ln x)^{n}\;dx={\frac {x^{m+1}(\ln x)^{n}}{m+1}}-{\frac {n}{m+1}}\int x^{m}(\ln x)^{n-1}dx\qquad {\mbox{(pentru }}m\neq -1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x}}={\frac {(\ln x)^{n+1}}{n+1}}\qquad {\mbox{(pentru }}n\neq -1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>n</mi> <mo>≠</mo> <mo>−</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x}}={\frac {(\ln x)^{n+1}}{n+1}}\qquad {\mbox{(pentru }}n\neq -1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9a3e555abd1d497d319629498f3872ef40ae7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:47.236ex; height:6.343ex;" alt="{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x}}={\frac {(\ln x)^{n+1}}{n+1}}\qquad {\mbox{(pentru }}n\neq -1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {\ln x\,dx}{x^{m}}}=-{\frac {\ln x}{(m-1)x^{m-1}}}-{\frac {1}{(m-1)^{2}x^{m-1}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>m</mi> <mo>≠</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {\ln x\,dx}{x^{m}}}=-{\frac {\ln x}{(m-1)x^{m-1}}}-{\frac {1}{(m-1)^{2}x^{m-1}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d8e72975a56e95ea6d4965cf519e9945b750285" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:66.457ex; height:6.176ex;" alt="{\displaystyle \int {\frac {\ln x\,dx}{x^{m}}}=-{\frac {\ln x}{(m-1)x^{m-1}}}-{\frac {1}{(m-1)^{2}x^{m-1}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x^{m}}}=-{\frac {(\ln x)^{n}}{(m-1)x^{m-1}}}+{\frac {n}{m-1}}\int {\frac {(\ln x)^{n-1}dx}{x^{m}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>m</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>m</mi> <mo>≠</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x^{m}}}=-{\frac {(\ln x)^{n}}{(m-1)x^{m-1}}}+{\frac {n}{m-1}}\int {\frac {(\ln x)^{n-1}dx}{x^{m}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529d176b9a8797878354cd222f48afcee13eba9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:76.909ex; height:6.676ex;" alt="{\displaystyle \int {\frac {(\ln x)^{n}\;dx}{x^{m}}}=-{\frac {(\ln x)^{n}}{(m-1)x^{m-1}}}+{\frac {n}{m-1}}\int {\frac {(\ln x)^{n-1}dx}{x^{m}}}\qquad {\mbox{(pentru }}m\neq 1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {x^{m}\;dx}{(\ln x)^{n}}}=-{\frac {x^{m+1}}{(n-1)(\ln x)^{n-1}}}+{\frac {m+1}{n-1}}\int {\frac {x^{m}dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>n</mi> <mo>≠</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {x^{m}\;dx}{(\ln x)^{n}}}=-{\frac {x^{m+1}}{(n-1)(\ln x)^{n-1}}}+{\frac {m+1}{n-1}}\int {\frac {x^{m}dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81ff92770f81d3acf1d01ecd585f79579a5d0bb2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:73.56ex; height:6.509ex;" alt="{\displaystyle \int {\frac {x^{m}\;dx}{(\ln x)^{n}}}=-{\frac {x^{m+1}}{(n-1)(\ln x)^{n-1}}}+{\frac {m+1}{n-1}}\int {\frac {x^{m}dx}{(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{x\ln x}}=\ln |\ln x|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{x\ln x}}=\ln |\ln x|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fad5afc489b105fe2750c7dc05449d516ec9214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.552ex; height:5.843ex;" alt="{\displaystyle \int {\frac {dx}{x\ln x}}=\ln |\ln x|}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{x^{n}\ln x}}=\ln |\ln x|+\sum _{i=1}^{\infty }(-1)^{i}{\frac {(n-1)^{i}(\ln x)^{i}}{i\cdot i!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msup> </mrow> <mrow> <mi>i</mi> <mo>⋅</mo> <mi>i</mi> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{x^{n}\ln x}}=\ln |\ln x|+\sum _{i=1}^{\infty }(-1)^{i}{\frac {(n-1)^{i}(\ln x)^{i}}{i\cdot i!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3ab2e4b3f937c722e3aea7e07e310b8ee3956ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:47.653ex; height:7.009ex;" alt="{\displaystyle \int {\frac {dx}{x^{n}\ln x}}=\ln |\ln x|+\sum _{i=1}^{\infty }(-1)^{i}{\frac {(n-1)^{i}(\ln x)^{i}}{i\cdot i!}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\frac {dx}{x(\ln x)^{n}}}=-{\frac {1}{(n-1)(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>x</mi> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>(pentru </mtext> </mstyle> </mrow> <mi>n</mi> <mo>≠</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>)</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\frac {dx}{x(\ln x)^{n}}}=-{\frac {1}{(n-1)(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/659561363b071bba0c3ec18ecb318e4f3e3d8e32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:52.582ex; height:6.176ex;" alt="{\displaystyle \int {\frac {dx}{x(\ln x)^{n}}}=-{\frac {1}{(n-1)(\ln x)^{n-1}}}\qquad {\mbox{(pentru }}n\neq 1{\mbox{)}}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)-\cos(\ln x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)-\cos(\ln x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69deb3cb5d25318bb2aefc68171e11c8af606bb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:40.904ex; height:5.676ex;" alt="{\displaystyle \int \sin(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)-\cos(\ln x))}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cos(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)+\cos(\ln x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cos(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)+\cos(\ln x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17c072211a492bf7b0d19ef53fb5309cfd4af3c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:41.16ex; height:5.676ex;" alt="{\displaystyle \int \cos(\ln x)\;dx={\frac {x}{2}}(\sin(\ln x)+\cos(\ln x))}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int e^{x}(x\ln x-x-{\frac {1}{x}})\;dx=e^{x}(x\ln x-x-\ln x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> </mrow> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int e^{x}(x\ln x-x-{\frac {1}{x}})\;dx=e^{x}(x\ln x-x-\ln x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a33a950bad713a5aa78667528b865b574c9242e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:47.589ex; height:5.676ex;" alt="{\displaystyle \int e^{x}(x\ln x-x-{\frac {1}{x}})\;dx=e^{x}(x\ln x-x-\ln x)}"></span></dd></dl>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Adus de la <a dir="ltr" href="https://ro.wikipedia.org/w/index.php?title=Primitivele_funcțiilor_logaritmice&oldid=7557829">https://ro.wikipedia.org/w/index.php?title=Primitivele_funcțiilor_logaritmice&oldid=7557829</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categorii" title="Special:Categorii">Categorii</a>: <ul><li><a href="/wiki/Categorie:Analiz%C4%83_matematic%C4%83" title="Categorie:Analiză matematică">Analiză matematică</a></li><li><a href="/wiki/Categorie:Calcul_diferen%C8%9Bial_%C8%99i_integral" title="Categorie:Calcul diferențial și integral">Calcul diferențial și integral</a></li><li><a href="/wiki/Categorie:Integrale" title="Categorie:Integrale">Integrale</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ultima editare a paginii a fost efectuată la 26 martie 2013, ora 07:53.</li> <li id="footer-info-copyright">Acest text este disponibil sub licența <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ro">Creative Commons cu atribuire și distribuire în condiții identice</a>; 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Primitivele funcțiilor logaritmice - Wikipedia