# Thread: Integrating a hyperbolic.

1. ## Integrating a hyperbolic.

Does anyone know how to integrate:

I've tried doing it in terms of e and I haven't really got anywhere.

Please help!

2. Originally Posted by Showcase_22
Does anyone know how to integrate:

I've tried doing it in terms of e and I haven't really got anywhere.

Please help!
You can multiply it with $\frac{tanh(x)}{tanh(x)}$

Remember that: $(\text{sech(x)})' = -\text{sech(x)}\text{tanh(x)}$

$tanh(x) = \sqrt{1-sech^2(x)}$

By substituting for u = sech(x), you will get a standard form in the end.

3. Originally Posted by Showcase_22
Does anyone know how to integrate:

I've tried doing it in terms of e and I haven't really got anywhere.

Please help!
$= \int \frac{2}{e^x + e^{-x}} \, dx$

and the substitution $u = e^x$ works just fine: $\int \frac{2}{u^2 + 1} \, du \, ....$

4. oh right. I think I tried turning it into partial fractions which is a very long and arduous process.

cheers!