# Thread: Power Series Representation of Improper Integral

1. ## Power Series Representation of Improper Integral

Find a power series representation for the improper integral:

$\displaystyle \int^{x}_{0}\frac{1-cost}{t^2}dt$

Almost done with my difficult homework but have no clue where to start here...thanks!

2. $\displaystyle cos(t) = 1- \frac{t^2}{2!}+\frac{t^4}{4!}-\frac{t^6}{6!}+\cdots$

sub this into the integral & simplfy