Help with Series Expansion

Hi - I ask for a bit of help in trying to find the series expansion of

Integral(arctan(x^3)) - I was having quite a bit of trouble, and eventually I was forced to look at Wolfram Alpha to get done with the homework, but I want to know where I messes up when I tried to do it.

Basically, this was where I started.

arctan x^3 = integral (1/(1-(-x^6)) dx

= Sum [(-1)^n*x^6n,n,0,infinity]

Then integrating both sides to get my answer, but this has been wrong.

Is my first step the bad part?