Primitive of Square of Hyperbolic Secant Function

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Theorem

$\displaystyle \int \sech^2 x \rd x = \tanh x + C$

where $C$ is an arbitrary constant.


Proof

From Derivative of Hyperbolic Tangent Function:

$\dfrac \d {\d x} \map \tanh x = \map {\sech^2} x$

The result follows from the definition of primitive.

$\blacksquare$


Sources