Question

How do you find the integral of `int x/((x^2 +2)^2) dx` from 0 to infinity?

Answer 1

`int_0^oo x/(x^2+2)^2dx = 1/2int_0^oo(2x)/(x^2+2)^2dx`

Let's `u = x^2+2`

So `du = 2xdx`

`1/2int_2^oo1/(u^2)du`

`-1/2[1/u]_2^oo`

`=-1/2(1/oo-1/2) = -1/2(0-1/2)`
`=1/4`