Question

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

Answer 1

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

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

$\Rightarrow \int \frac{dz}{z^2+1}$ [let z = $e^x$ ]

$\Rightarrow ta{n}^{-1}\left(z\right)+c$ [c is arbitrary constant]

$\Rightarrow ta{n}^{-1}\left(e^x\right)+c$