Question

Find the power expansion for integral 1/(x^7 + 1) dx for |x| < 1.

Answer 1

\[\frac{1}{1-x}=\sum_{n=0}^{\infty}x^n\] replace \(x\) by \(-x^7\)

Answer 2

first step is to write
\[\sum_{n=0}^{\infty}((-x)^7)^n\] the clean up with some algebra

Answer 3

could write it as
\[\sum_{n=0}^{\infty}(-1)^nx^{7n}\]

Answer 4

oop it was the integral. so there is one more step, take the expansion written above and integrate it term by term

Answer 5

Thanks!

Answer 6

yw