Question

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

Answer 1

$\begin{array}{cc}\int \frac{dx}{e^x+e^{-x}}& \\ \Rightarrow \int \frac{e^x}{e^{2x}+1}dx& put;e^x=t\\ \Rightarrow \int \frac{1}{t^2+1}dt& e^{x}dx=dt\\ \Rightarrow {\tan }^{-1}t+c& \\ \Rightarrow {\tan }^{-1}{e}^x+c& \end{array}$

Hence, this is the answer.