# Representing a function as a power series

1. Apr 27, 2008

### grothem

1. The problem statement, all variables and given/known data
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?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Apr 27, 2008

### Dick

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.

3. Apr 28, 2008

### grothem

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?

4. Apr 28, 2008

### Dick

That's one way to get a series for arctan, yes. But you forgot a (-1)^n factor. The expansion of 1/(1-x) has all plus signs. 1/(1+x) doesn't.