1. ## Improper Integrals

the problem is: int(x/((x^2+2)^2)dx) from 0 to infinite

I just have to tell whether it's convergent or divergent. I set it to the
lim as t-> infinite of the integral from 0 to t. I'm having trouble integrating it. I started using partial fractions but can't anywhere with that. Any help would be appreciated.

Make the substitution $u=x^2+2\implies \,du=2x\,dx$
The integral transforms from $\int_0^{\infty}\frac{x}{\left(x^2+2\right)^2}\,dx\ implies \tfrac{1}{2}\int_2^{\infty}\frac{\,du}{u^2}$