Write a value

Question:

Write a value of $\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x$.

Solution:

given $\int e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right) d x$

$=\int \frac{e^{x}}{x} d x-\int \frac{e^{x}}{x^{2}} d x$

$=\int \frac{e^{x}}{x} d x-\left[\frac{e^{x}}{x^{2}}-\int-\frac{e^{x}}{x}\right]+c$

$=-\frac{e^{x}}{x^{2}}+c$

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