1. The problem statement, all variables and given/known data Evaluate the indefinite integral as a power series and find the radius of convergence [tex]\int\frac{x-arctan(x)}{x^3}[/tex] 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
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) = [tex]\int\frac{1}{1+x^2}[/tex] = [tex]\int\sum (x^(2*n))[/tex] = [tex]\sum\frac{x^(2(n+1)}{2(n+1)}[/tex] is this what you mean?
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.