sin-2tan-1-x-x-x-the-limit-0- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 127885 by psyche last updated on 02/Jan/21 ∫(sin(2tan−1(x)+x)x)thelimit[0,∞) Answered by Lordose last updated on 02/Jan/21 Ω=∫0∞sin(2tan−1(x)+x)xdxsin(2tan−1(x)+x)=sin(2tan−1(x))cos(x)+cos(2tan−1(x))sin(x)N.B::(sin(2tan−1(x))=2x1+x2cos(2tan−1(x))=1−x21+x2)Ω=∫0∞11+x2(2xcos(x)+(1−x2)sin(x))xΩ=∫0∞2cos(x)1+x2dx+∫0∞sin(x)x(1+x2)dx−∫0∞xsin(x)1+x2dxΩ=2⋅π2e+∫0∞sin(x)x(1+x2)dx−∫0∞sin(x)xdx+∫0∞sin(x)x(1+x2)dxΩ=πe−π2+2ΦΦ=∫0∞sin(x)x(1+x2)dx=π2(1−e−1)Ω=πe−π2+π−πe=π2★\boldsymbolLϕrD\boldsymbol∅sE Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-62347Next Next post: Question-127887 Leave a Reply Cancel replyYour email address will not be published.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.