find-the-value-of-0-x-ch-x-dx- Tinku Tara June 3, 2023 Integration 0 Comments FacebookTweetPin Question Number 66786 by mathmax by abdo last updated on 19/Aug/19 findthevalueof∫0∞xch(x)dx Commented by mathmax by abdo last updated on 20/Aug/19 letI=∫0∞xch(x)dx⇒I=∫0∞2xex+e−xdx=∫0∞2xe−x1+e−2xdx=2∫0∞xe−x(∑n=0∞(−1)ne−2nx)dx=2∑n=0∞(−1)n∫0∞xe−(2n+1)xdx=(2n+1)x=t2∑n=0∞(−1)n∫0∞t2n+1e−tdt2n+1=2∑n=0∞(−1)n(2n+1)2∫0∞te−tdtbut∫0∞te−tdt=Γ(2)=1!=1⇒I=2∑n=0∞(−1)n(2n+1)2….becontinued… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: find-the-value-of-0-x-2-ch-x-dx-Next Next post: sove-the-de-1-2-x-y-x-x-1-y-xsin-2x- Leave a Reply Cancel replyYour email address will not be published.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.