Question

Integrate the function $e^x(\frac{1}{x}-\frac{1}{x^2})$

Answer 1

Let $I=\int e^x[\frac{1}{x}-\frac{1}{x^2}]dx$
now let $\frac{1}{x}=f\left(x\right)\Rightarrow f^{\prime }\left(x\right)=\frac{-1}{x^2}$
Also we know that, $\int e^x\left\{f\right(x)+f^{\prime }(x\left)\right\}dx=e^{x}f\left(x\right)+C$
$\therefore I=\frac{e^x}{x}+C$