Quick power series question

Hi I was wondering if anyone could guide me through this question:

Find a power series representation of the function of $\displaystyle f(x) = \int_{0}^{\infty }\frac{sin(t)}{t}dt$ using termwise integration of the Maclaurin series for sin x. For which xER is this representation valid.

Thank you in advance :)

Re: Quick power series question

Quote:

Originally Posted by

**Dragonkiller** Hi I was wondering if anyone could guide me through this question:

Find a power series representation of the function of $\displaystyle f(x) = \int_{0}^{\infty }\frac{sin(t)}{t}dt$ using termwise integration of the Maclaurin series for sin x. For which xER is this representation valid.

Thank you in advance :)

Don't you know the MacLaurin series for sin(t)? Just divide every term by t, then integrate...