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Video, matematikte belirsiz integral hesaplama tekniklerini öğrenmek isteyenler için faydalı bir kaynaktır."]},"endTime":397,"title":"Belirsiz İntegral Hesaplama Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral Sorununun Tanıtımı","list":{"type":"unordered","items":["Sorulan integral: iki üzeri x'in doğal logaritması bölü x dx'in belirsiz integrali.","İntegralde x'in doğal logaritması üs olarak görülür ve bir ifade ile onun türevi bulunur.","İntegralde yerine koyma metodu uygulanabilir çünkü bir ifade ve türevi var."]},"beginTime":2,"endTime":46,"href":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=2&ask_summarization=1"},{"index":1,"title":"Yerine Koyma Yöntemi","list":{"type":"unordered","items":["Yerine koyma metodunda u = x'in doğal logaritması olarak tanımlanır ve du/dx = 1/x olur.","İntegralde 1/x dx yerine du yazılır ve integral 2 üzeri u du şeklinde sadeleşir.","Bu integral hala kolay görünmese de, e üzeri x'in integralinin e üzeri x artı c olduğunu bilmek yardımcı olabilir."]},"beginTime":46,"endTime":129,"href":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=46&ask_summarization=1"},{"index":2,"title":"Üslü İfadelerle İşlem","list":{"type":"unordered","items":["2, e üzeri 2'nin doğal logaritması olarak yazılabilir.","İntegralde 2 üzeri u yerine e üzeri (2'nin doğal logaritması × u) yazılır.","Üssün üssü kuralı kullanılarak e üzeri (2'nin doğal logaritması × u) = e üzeri a×u şeklinde yazılır ve a = 2'nin doğal logaritması olarak tanımlanır."]},"beginTime":129,"endTime":198,"href":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=129&ask_summarization=1"},{"index":3,"title":"İntegralin Çözümü","list":{"type":"unordered","items":["İntegral e üzeri a×u'nun integrali olarak yazılır ve cevabı 1/a × e üzeri a×u + c olur.","a = 2'nin doğal logaritması olduğu için cevap 1/(2'nin doğal logaritması) × e üzeri (2'nin doğal logaritması × u) + c olur.","e üzeri (2'nin doğal logaritması × u) = 2 üzeri u olduğundan, cevap 1/(2'nin doğal logaritması) × 2 üzeri u + c olur."]},"beginTime":198,"endTime":367,"href":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=198&ask_summarization=1"},{"index":4,"title":"Sonuç","list":{"type":"unordered","items":["u = x'in doğal logaritması olduğu için, son cevap 1/(2'nin doğal logaritması) × 2 üzeri (x'in doğal logaritması) + c olur."]},"beginTime":367,"endTime":391,"href":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=367&ask_summarization=1"}],"linkTemplate":"/video/preview/13895522588354252284?parent-reqid=1769616715832197-12569738840988749270-balancer-l7leveler-kubr-yp-vla-186-BAL&text=LN+X+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"(2^ln x)/x Ters Türev Örneği (Kalkülüs)","related_orig_text":"LN X - 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