# Representing a function as a power series

## Homework Statement

Evaluate the indefinite integral as a power series and find the radius of convergence

$$\int\frac{x-arctan(x)}{x^3}$$

I have no idea where to start here. Should I just integrate it first?

## The Attempt at a Solution

Dick
Homework Helper
Sure, you could do that. But, I think what they want to do is expand arctan(x) as a power series around 0 and then integrate.

ok. So arctan(x) = $$\int\frac{1}{1+x^2}$$
= $$\int\sum (x^(2*n))$$
= $$\sum\frac{x^(2(n+1)}{2(n+1)}$$

is this what you mean?

Dick