# Power series

Evaluate the indefinite integral as a power series and find radius of convergence. (i don't know how to type the integral and summations signs, sorry)

(integral sign) (x-tan^-1x)/x^3 dx. ( if you write this out it makes more sense)

i was able to find the power series of tan^-1x = x^(2n+1) (-1)^n/(2n+1).
i don't know how to continue on with this. all we have learned is to use the power series of the geometric series 1/(1-x), and some integration/differentiation methods.

i am rather confused on the whole topic, so if anyone has any ideas, the simplest explanations would be greatly appreciated. thanks

## Answers and Replies

dextercioby
Homework Helper
So your integral is
$$\int \frac{x-\arctan x}{x^{3}} dx$$

??Okay,for term by term integration of it,separate it into 2 integrals...Though it's not really helpful for the convergence part...

Daniel.

that is the integral, thanks, but i am not sure what to do after pulling it apart into two integrals. quite honestly, i am puzzled by this whole topic. any advice?

dextercioby