# Homework Help: Integration by parts

1. Feb 1, 2010

### apiwowar

the problem is find the integral of xarctan(x^2)dx

i set w = x^2, so 1/2dw = xdx

then i plug that into the integral to get

the integral of 1/2arctan(w)dw

so i let u = arctan(w) and dv = dw
so du = dw/(1+w^2) and v = w

so then the integral of udv = uv - integral of vdu

so 1/2(w*arctan(w) - integral of w * 1/(1+w^2)dw is what i end up with

but then if i would have to do integration by parts on the second integral

which gets me at

1/2(w*arctan(w) - wln(1+w^2) - integral of ln(1+w^2)dw

and that gets me stuck due to the having to take the antiderivative of the natural log

any help would be appreciated. and sorry if its hard to read

2. Feb 2, 2010

### vela

Staff Emeritus
You can do the second integral using the substitution u=w2+1. You don't need to integrate by parts.