Question

find power series (maclaurin series):
integral [ ln(1+x^2) ] dx

Answer 1

What are the limits on the integral? if any

Answer 2

Ah just realized you don't need to have a definite integral...

Recall the power series for \(\ln(1+x)\):
\[\ln(1+x)=\sum_{k=1}^\infty \frac{(-1)^{k+1}x^k}{k}\quad(|x|<1)\]
Replace \(x\) with \(x^2\), then take the antiderivative of the series.

Answer 3

yeah... i was hoping someone would actually do the dirty work though and show me

Answer 4

You and most of everyone else