I don't think we're expected to know how to do a power series. I don't quite understand what you're suggesting to do. I looked at it again and tried to do two separate integrals
t/(1+t^2)dt - (tan(t))/(1+t^2)dt. It seems to be yielding no results at this point
Homework Statement
Lim (x→0) [ x^(-8) ∫ (0 to x^2) of (t-tan(t))/(1+t^2)dt ]
Homework Equations
The Attempt at a Solution
My first thought was to find the integral, then put (x^(-8)) into the solution of the integral and then do the limit.
I tried doing the substitution rule equating u=...