I'm supposed to use an infinite series to solve $$\int\frac{e^{2x}}{x}dx$$
How do I solve this? I know the answer already, I don't even have to use infinite series to solve this, however it was specifically instructed to have it solved by using infinite series.
Recall the power series for $e^{x}$ is $$e^x = 1+\frac{x}{1!}+\frac{x^2}{2!}+\dotsb + \frac{x^k}{k!}+\dotsb$$ Use this to get the series for $\frac{e^{2x}}{x}$ and then integrate term by term.