Residue theorem problem involving real value Intergral

[xdrgnh]

Homework Statement

∫ from infinity to 0 of x^2/(x^2+1)(x^2+16)

Homework Equations

The Integral will be the sum of the residues times 2πi

The Attempt at a Solution

The only singularities that matter are at i and 4i and they are simple poles. So x^2/(x^2+1)/(2x) and I plug in 4i and get -2i/(15) then I plug in i into x^2/(x^2+16)/(2x) and get i/30 and when I add them I get -3i/30. Because it's only from 0 and to negative infinity I mult that by ∏i and I get ∏/10.

 

[vela]

Looks good.

You glossed over several steps, which I'm assuming you understand. Just make sure you know why you can do what you did.