prove-that-1-0-1-t-p-ln-t-t-1-dt-pi-2-6-k-1-p-1-k-2-2-0-1-t-2p-ln-t-t-2-1-dt-pi-2-8-k-0-p-1-1-2k-1-2- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 40885 by prof Abdo imad last updated on 28/Jul/18 provethat1)∫01tpln(t)t−1dt=π26−∑k=1p1k22)∫01t2pln(t)t2−1dt=π28−∑k=0p−11(2k+1)2 Commented by math khazana by abdo last updated on 02/Aug/18 1)∫01tpln(t)t−1dt=−∫01tpln(t)(∑n=0∞tn))dt=−∑n=0∞∫01tn+pln(t)dt=−∑n=0∞AnandbypartsAn=∫01tn+pln(t)dt=[1n+p+1tn+p+1ln(t)]01−∫011n+p+1tn+pdt=−1(n+p+1)2⇒−∑n=0∞An=∑n=0∞1(n+p+1)2=n+p+1=k∑k=p+1∞1k2but∑k=1∞1k2=π26=∑k=1p1k2+∑k=p+1∞1k2⇒∑k=p+1∞=π26−∑k=1p1k2=∫01tpln(t)t−1dt. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-0-t-p-e-t-1-dt-with-p-N-Next Next post: prove-that-0-1-t-2p-1-ln-t-t-2-1-dt-pi-2-24-1-4-k-1-p-1-k-2- Leave a Reply Cancel replyYour email address will not be published.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.