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