Question:
$e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)$
Solution:
Let $I=\int e^{x}\left[\frac{1}{x}-\frac{1}{x^{2}}\right] d x$
Also, let $\frac{1}{x}=f(x) \Rightarrow f^{\prime}(x)=\frac{-1}{x^{2}}$
It is known that, $\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+\mathrm{C}$
$\therefore I=\frac{e^{x}}{x}+\mathrm{C}$