find-cos-tx-1-x-2-2-dx-with-t-0- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 33986 by abdo imad last updated on 28/Apr/18 find∫−∞+∞cos(tx)(1+x2)2dxwitht⩾0 Commented by math khazana by abdo last updated on 01/May/18 letintroducethecomplexfunctionφ(z)=eitz(1+z2)2wehaveI=∫−∞+∞cos(tx)(1+x2)2dx=Re(∫−∞+∞eitx(1+x2)2dx)φ(z)=eitz(z−i)2(z+i)2sothepolesofφareiand−i(doubles)∫−∞+∞φ(z)dz=2iπRes(φ,i)Res(φ,i)=limz→i1(2−1)!((z−i)2f(z))′=limz→i(eitz(z+i)2)′=limz→iiteitz(z+i)2−2(z+i)eitz(z+i)4=limz→i(z+i)iteitz−2eitz(z+i)3=(2i)ite−t−2e−t(2i)3=−4e−t−8i=12ie−t∫−∞+∞φ(z)dz=2iπe−t2i=πe−t⇒I=πe−t Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: calculate-0-1-1-x-ln-1-x-1-x-dx-Next Next post: find-cos-x-1-x-2-3-dx-with-0- Leave a Reply Cancel replyYour email address will not be published.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.