Question

Need help solving this integral.

$\int_{-\infty}^{\infty} \frac{cos(4x))}{x^2+2x+2}dx$

Answer 1

cos 4x Arsy da x² + 2x42 i cosya or42 da S (x - 2)2 + 4 13 Site i casua 213-1+1) dra 2174 +i+1) da 2 į S cosya da x-it Cos 42 x +i+) 7 84 CJ 470 da Now solving atit du =1 dhi ydy=dx substitute 4x titi Cosly 4-4 1-4) da u SCIENCI OLYMPIAD FOUNDATION = sin (uity) sinuut coluitu) cosyu dy J u sincity) sinua cos (uity) cos44 du Jesinkitys sinya t u sincity) sinuity) p sinyudu + cos(uitu) i cosuu du ༥) ༼ ག ད པ Now solving sinyu du du=- dv u substitute yu 9 sinu dv Se Silv) V Now folving S Cos yu du u A substitute v=uu cosu dv Scanned with CS CamScanner duz tev Ci(v) I cosu

Plug in solved Integrals. sintuitys j sinu sinya du + Cosluitus siens can you to こ Cos 141-4) Ciluu) sinlui-u) si (44) undo substitution ų=x-it Colu-u) Cil 4(x+1) - sin(yiny) si (41*-*+1) in solved Cosua da atiti X-it plug cosua da integrals - 7 S i sin luitu) silylatiti) i cos (4+4) Ci(4191+i+1) + 2 2 tisinlui-4) si (ylgniti) i cos (41–4) Cí (4(0-1+i)) 2 QUYONNO CVIWAZO DNIDS 2 The problem is solved Afta Substitution lowes and uppes limit me get Tcosy еч gut 1 Cos ya x²+2x+2 da = S CS Scanned with CamScanner