The question asks to show using the residue theorem that(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int[/itex]cos(x) / (x^{2}+1)^{2}dx = [itex]\pi[/itex] / e

(the terminals of the integral are -∞ to ∞ but i didnt know the code to write that)

I found the singularities at -i and +i

so i think we change the function inside the integral to cos(z) / (z^{2}+1)^{2}

i expanded the cos(z) as cosh(1) - isinh(1)(z-i) -0.5cosh(1)(z-i)^{2}+...

and i expanded (z^{2}+1)^{2}as -(1/4)(z-i)^{2}- i/4(z-i) + 3/16 +...

I did the same for the singularity at x=-i and when i added both the residues together i got

(9/16e + e/16) (this is multiplied by 2[itex]\pi[/itex]i to find residues)

this doesnt seem right? i dont know if what ive done is the right method. please help, ive spent soooo many hours on this one stupid question :(

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# Homework Help: Integral using residue theorem

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