Improper Integrals, Specifically integration part

[max023]

Homework Statement

Find the antiderivative of (x*arctan(x))/(1+x^2)^2)

The Attempt at a Solution

I've had a few attempt at this (I've been working on it an embarrassingly long time) but i felt most on track doing it by parts. Here's how i went

u = arctan(x)
du = 1/(1+x^2)*dx

dv = x/(1+x^2)^2
let m = 1+x^2
dm = 2x*dv
v = 1/2*S(1/m^2)*dm
subbing values back in
v = (-1/6)*(1+x^2)^(-3)

placing it all in uv-S(v*du)

(1/6)*arctan(x)*(1+x^2)^(-3)-(1/6)*S(1/(1+x^2)^(4)*dx)

Is it possible to integrate S(1/(1+x^2)^(4)*dx) easily? I thought you needed an x somewhere on top to do it by partial fractions. If no one has the time to answer this thanks anyway.

 

[HallsofIvy]

No, you do not "need an x somewhere on top".