Primitive of Square of Hyperbolic Secant Function

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Theorem

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

where $C$ is an arbitrary constant.


Proof

From Derivative of Hyperbolic Tangent:

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

The result follows from the definition of primitive.

$\blacksquare$


Sources