Compute the integral $\int\frac{e^x}{x}\mathrm dx$

Question

I need helping computing the following indefinite integral $$\int\frac{e^x}{x}\mathrm dx$$

I tried integration by parts but did not yield any result.

Answer 1

$\int\dfrac{e^x}{x}dx$

$=\int\dfrac{1}{x}\sum\limits_{n=0}^\infty\dfrac{x^n}{n!}dx$

$=\int\sum\limits_{n=0}^\infty\dfrac{x^{n-1}}{n!}dx$

$=\int\left(\dfrac{1}{x}+\sum\limits_{n=1}^\infty\dfrac{x^{n-1}}{n!}\right)dx$

$=\ln x+\sum\limits_{n=1}^\infty\dfrac{x^n}{n!n}+C$