# What is the power series representation of $\int \frac{4e^{-x}-4}{x}$

What is the power series representation of $\int \frac{4e^{-x}-4}{x}$

I am having trouble solving this problem for my Calculus 2 class. I have attempted to split apart the integrand and solve it that way, but to no avail. Preferably, I would like the final answer to have the starting index of n=1. Steps would also be greatly appreciated.

## 1 Answer

Can you write power series representation of $e^{-x}$?

$$4\int \frac{e^{-x}-1}{x} = 4 \int \frac{(1-x+x^2/2\cdots)- 1}{x}$$

• Your integrand is different from what I originally put. The "e" is raised to a negative "x". Nov 5 '17 at 23:45
• Thanks, corrected. Nov 5 '17 at 23:50