Expand Arctanx as a power series around 0 and integrate. You 'll get a new power series, whose radius of convergence can be calculated by the 1/limsup formula.
I've found a more challenging integral. I had trouble figure this one out.
Evaluate the indefinite integral as a power series. What is the radius of convergence?
the arctangent through me off.
also, INT (x - arctan x)/ x^3 dx