# Thread: integral method for rational functions of sinh and cosh

1. ## integral method for rational functions of sinh and cosh

I have a feeling I should know this, but what's the method for finding the integral of functions like

$\displaystyle \int \frac{1}{\sinh x + 2\cosh x} \, dx$

This is easy is it were regular trigonometric functions (using the famous tan substitution) but how do we approach these one?

No need to solve the problem, I'm just asking about the method

Regards,

Stonehambey

2. Originally Posted by Stonehambey
I have a feeling I should know this, but what's the method for finding the integral of functions like

$\displaystyle \int \frac{1}{\sinh x + 2\cosh x} \, dx$

This is easy is it were regular trigonometric functions (using the famous tan substitution) but how do we approach these one?

No need to solve the problem, I'm just asking about the method

Regards,

Stonehambey
The first thing I'd do is replace the hyperbolic functions with their exponential definitions.

Alternatively, you could probably use the less famous tanh substitution.

3. tanh substitution? I've never heard of that one before.

4. Originally Posted by Stonehambey
tanh substitution? I've never heard of that one before.
Well, I did say it was less famous. It's in here: 4.