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use the contour integration and theory of residues to evaluate too COS Xdx -O [1+ x41

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Since the answer is too lengthy there will be some chance of some errors(I have avoided every errors as much i can)So please go through the answers and understand each step 1- x de +1 f = & cost [241=0 (x-7)(x-e14) (x-e374) 2= + (),+C) (x- & BA 18 f(z) = z s + (2-2%) (22%) (2-2°%) (2_213) R & ficante = + sorte - 211ickes fez). -, . Residue ane @ = eit and 2. & 3 is available Res = e = 4:1 (2 - eT4) ek Dr.CENY 2.21%)(-+ 1x) = (12) (V2 + Vai) (2) - (en 14 ) (z-e 5 -2/2 +2r2i 21C2+i) Similaly Res 2- 13/4 - e 3 (E _ +1/4) C B 1974137 꼫 231231 -2iGe | [ ] 쪽쪽 금음가표기기food - ez az ter to Receiz) d i Rete 2) K + Then Lel los then z= Re: dz=iRe e do U ios Recedo) O py te Denominetos - / let =NR IRC Cos&tising) .:Reis / - / R Creatitisan 10 -circest ller sind Here & us from o Sind us this sange is the positive cobebdz 24+) ris nz ca Real part of Sflzzaz V -

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