# Intgeration by parts problem

#### shadow dancer

Hello, I can't solve this integral which is in Pikunov's book . It says use integration by parts, but I can't solve it.
Problem is $$\int \frac{x \arctan(x)}{(1+x^2)^2} \,dx$$ thank U by the way.

#### idontknow

Start with $$\displaystyle x=\tan(v)$$.

#### idontknow

$$\displaystyle dx=sec^2 (v) dv \;$$
 $\int \frac{x \arctan(x)}{(1+x^2)^2} \,dx =\int v\tan(v)\cos^4 (v) sec^2 (v) dv =\int v\sin(v)\cos(v)dv= \dfrac{\sin\left(2v\right)-2v\cos\left(2v\right)}{8}+C$. $v\sin(v)\cos(v)dv=\dfrac{2v}{4}\sin(2v) dv$.

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