Finding Indefinite Integral of a combination of hyperbolic functions

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Homework Statement

Compute the following:

$\int \frac{cosh(x)}{cosh^2(x) - 1}\,dx$

Homework Equations

$\int cosh(x)\,dx = sinh(x) + C$

The Attempt at a Solution

I had no clue where to start, so I went to WolfRamAlpha, and it used substitution but it made $u = tanh(\frac{x}{2})$ and I had no clue how I am supposed to know to do that.

Any advice on where to start is greatly appreciated.

 

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I solved this problem after realizing that $cosh^2(x) - 1 = sinh^2(x)$. This allowe me to split make it $\int coth(x)csch(x)\,dx$, and then I could use another identity to set that equal to $-csch(x) + c$