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Inverse hyperbolic cotangent

The inverse hyperbolic cotangent is written with logarithms as

Area functions can be described with logarithms because all hyperbolic functions are defined by exponential functions.

 

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Explanation

We'll start with the hyperbolic cotangent

Substitution of e^θ = k gives

We continue only with the positive solution and substitute k = e^θ so that

Now we take the logarithm from both sides

Substitution of θ = arcoth x gives

 

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