Primitive of Hyperbolic Secant Function
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Theorem
Arcsine Form
- $\ds \int \sech x \rd x = \map \arcsin {\tanh x} + C$
Arctangent of Hyperbolic Sine Form
- $\ds \int \sech x \rd x = \map \arctan {\sinh x} + C$
Arctangent of Exponential Form
- $\ds \int \sech x \rd x = 2 \map \arctan {e^x} + C$
Arctangent of Half Hyperbolic Tangent Form
- $\ds \int \sech x \rd x = 2 \map \arctan {\tanh \dfrac x 2} + C$