Question

Evaluate:

$\int \frac{1}{e^x+e^{-x}}dx$.

Answer 1

Now,

$\int \frac{1}{e^x+e^{-x}}dx$

$=\int \frac{e^x}{e^{2x}+1}dx$

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

$={\tan }^{-1}\left(e^x\right)+c$ [ Where $c$ is integrating constant]