Primitive of Hyperbolic Secant Function/Arctangent of Exponential Form

Theorem

 * $\displaystyle \int \operatorname{sech} x \ \mathrm d x = 2 \arctan \left({e^x}\right) + C$

Proof
Let:

Let:

Then:

Also see

 * Primitive of Hyperbolic Secant Function/Arcsine Form


 * Primitive of Hyperbolic Cosecant Function