# Finding a power series expansion for a definite integral

1. Mar 12, 2012

### Szichedelic

1. The problem statement, all variables and given/known data

Find a power series expansion about x = 0 for the function

f(x) = $^{1}_{0}\int\frac{1 - e^{-sx}}{s}$ ds

2. Relevant equations

The power series expansion for a function comes of the form f(x) = $^{\infty}_{0}\sum a_{k}x^{k}$

3. The attempt at a solution

I've tried several things to start off with but quickly end up hitting a dead end road. First, I tried just simply taking the integral, but quickly found it isn't defined at 0 (hence why they are asking me to find a power series expansion for it). Then, I tried finding a power series expansion for the innerpart of the integral and ran into the same problem.

2. Mar 12, 2012

### LCKurtz

Did you try substituting the Taylor series (as a function of x) for $e^{-sx}$ in the integrand, simplifying and integrating?

3. Mar 13, 2012

### Szichedelic

Yeah, I figured that out shortly after I posted this. Can't believe I overlooked that! Thanks!