1-x-lnt-1-t-2-dt- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 91220 by Ar Brandon last updated on 28/Apr/20 ∫1xlnt1+t2dt Commented by abdomathmax last updated on 28/Apr/20 lettakeatryifx>1wedothechangementt=1u⇒I=−∫1x1−lnu1+1u2(−duu2)=−∫1x1lnu1+u2du=−∫1x1lnu(∑n=0∞(−1)nu2n)du=∑n=0∞(−1)n+1∫1x1u2nlnudu=∑n=0∞(−1)n+1UnUn=∫1x1u2nln(u)du=byparts[u2n+12n+1lnu]1x1−∫1x1u2n2n+1du=12n+1lnxx2n+1−12n+1[12n+1u2n+1]1x1=ln(x)(2n+1)x2n+1−1(2n+1)2(1−1x2n+1)⇒I=−lnx∑n=0∞(−1)n(2n+1)x2n+1+∑n=0∞(−1)n(2n+1)2−∑n=0∞(−1)n(2n+1)2x2n+1resttocalculatethosesumsifx<1I=−∫x1lnt1+t2dt=−∫x1lnt(∑n=0∞(−1)nt2n)dt=−∑n=0∞(−1)n∫x1t2nlntdtandwefollowthesameway….becontinued… Commented by Ar Brandon last updated on 28/Apr/20 �� Commented by mathmax by abdo last updated on 29/Apr/20 thankx Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: For-a-geosynchronous-satellite-of-mass-m-moving-in-a-circular-orbit-around-the-earth-at-a-constant-speed-v-and-an-altitude-h-above-the-earth-surface-Show-the-velocity-v-GM-e-R-e-h-1-2-INext Next post: what-is-complementary-error-function-erfc-t- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.