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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.

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

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

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

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