Question

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

Answer 1

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

Let $e^x=t⟹e^{x}dx=dt$

Then $I=\int \frac{dt}{t^2+1}={\tan }^{-1}t+C={\tan }^{-1}{e}^x+C$