find-0-ln-1-t-2-t-2-dt- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 32478 by prof Abdo imad last updated on 25/Mar/18 find∫0∞ln(1+t2t2)dt Commented by prof Abdo imad last updated on 30/Mar/18 I=∫0+∞ln(1+1t2)dtbypartsI=][tln(1+1t2)]0+∞−∫0+∞t−2t3(1+1t2)−1dt=2∫0∞1t2.11+1t2dt=2∫0∞dtt2+1=2π2=πletprovethatlimt→+∞tln(1+1t2)=0=limu→01uln(1+u2)=limu→∞uln(1+u2)u2=0alsolimt→otln(1+1t2)=limt→0tln(1+t2)−2tlnt=0finallyI=π Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-32474Next Next post: Lambert-series-type-representation-for-1-factorial-i-i-i-i-1-2-n-1-1-n-e-n-2-1- Leave a Reply Cancel replyYour email address will not be published.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.