Primitive of Hyperbolic Secant of a x

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Theorem

Arcsine Form

$\ds \int \sech a x \rd x = \frac {\map \arcsin {\tanh a x} } a + C$


Arctangent of Hyperbolic Sine Form

$\ds \int \sech a x \rd x = \frac {\map \arctan {\sinh a x} } a + C$


Arctangent of Exponential Form

$\ds \int \sech a x \rd x = \frac {2 \map \arctan {e^{a x} } } a + C$


Also see