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Inverse Hyperbolic Functions

In this post we define Inverse Hyperbolic Functions. The inverse hyperbolic Functions are expressed in terms of natural logarithms.

Sinh-1 x ln(x+\sqrt{x^2+1})  For all x
Cosh-1 x ln(x+\sqrt{x^2-1}), x\geq 1
Tanh-1 x \frac{1}{2}ln(\frac{1+x}{1-x}), |x|<1
Cosech-1 x ln(\frac{1}{x}+\frac{\sqrt{1+x^2}}{|x|}), x \neq 0
Sech-1 x ln(\frac{1}{x}+\frac{\sqrt{1-x^2}}{x}), 0<x \leq 1
Coth-1 x \frac{1}{2}ln(\frac{1-x}{1+x}), |x|<1


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