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Question Number 169864 by mathlove last updated on 11/May/22
Answered by Mathspace last updated on 11/May/22
(3x)=t⇒x=t3⇒∫01(...)(...)dx=∫01tt(3t2)dt=3∫01tt+2dt=3∫01e(t+2)lntdt=3∫01∑n=0∞(t+2)n(lnt)nn!dt=3∑n=0∞1n!∫01(t+2)n(lnt)ndtor∫01(t+2)n(lnt)ndt=∫01∑k=0nCnktk2n−k(lnt)ndt=∑k=0n2n−kCnk∫01tk(lnt)ndt=...
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