Question

Solve $\int \frac{dx}{(e^x+e^{-x}{)}^2}$.

Answer 1

$\int \frac{dx}{(e^x+e^{-x}{)}^2}$

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

Let $e^{2x}+1=m$

$2e^{2x}dx=dm$

$\int \frac{dm}{2m^2}$

$⟹-\frac{1}{2m}$

$I=-\frac{1}{2(e^{2x}+1)}+c$