# Representing a function as a power series

by grothem
Tags: function, power, representing, series
 P: 23 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
 Sci Advisor HW Helper Thanks P: 25,250 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.
 P: 23 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?
 Sci Advisor HW Helper Thanks P: 25,250 Representing a function as a power series 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.

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