# integral method for rational functions of sinh and cosh

• Apr 26th 2009, 04:58 AM
Stonehambey
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

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

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
• Apr 26th 2009, 05:25 AM
mr fantastic
Quote:

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

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

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.
• Apr 26th 2009, 11:18 PM
Stonehambey
tanh substitution? I've never heard of that one before.
• Apr 27th 2009, 03:18 AM
mr fantastic
Quote:

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.