Primitive of Square of Hyperbolic Secant Function

Theorem

 * $\displaystyle \int \operatorname{sech}^2 x \ \mathrm d x = \tanh x + C$

where $C$ is an arbitrary constant.

Proof
From Derivative of Hyperbolic Tangent Function:
 * $\dfrac{\mathrm d}{\mathrm dx} \tanh \left({x}\right) = \operatorname{sech}^2 \left({x}\right)$

The result follows from the definition of primitive.