Question:
Write a value of $\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x$.
Solution:
given $\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x$
$=\int \frac{e^{x}}{x} d x-\int \frac{e^{x}}{x^{2}} d x$
$=\int \frac{e^{x}}{x} d x-\left[\frac{e^{x}}{x^{2}}-\int-\frac{e^{x}}{x}\right]+c$
$=-\frac{e^{x}}{x^{2}}+c$