# Help integrating 1/(cosh(z)+1)

1. Apr 6, 2014

### Jarfi

1. The problem statement, all variables and given/known data

integrate 1/(cosh(z)+1)

2. Relevant equations

3. The attempt at a solution

integral(1/(cosh(z)+1))=arctan((cosh(z)) but can I also do 1/(cosh(z)+1)=cosh(z)-1/sinh(z) and go from there and get a simpler solution or something?

2. Apr 6, 2014

### vela

Staff Emeritus
Do you mean
$$\int \frac{dz}{\cosh z + 1} = \text{arctanh}\cosh z$$ and
$$\frac{1}{\cosh z+1} = \frac{\cosh z-1}{\sinh^2 z}.$$ The first one I figure was a typo, but I don't see how you got your second expression, the one for 1/(cosh z + 1)

Last edited: Apr 7, 2014
3. Apr 6, 2014

### SammyS

Staff Emeritus
$\sinh^2 z = \cosh^2 z - 1$

4. Apr 6, 2014

### vela

Staff Emeritus
But how did the OP get 1/(cosh(z)+1)=cosh(z)-1/sinh(z)?

5. Apr 6, 2014

### SammyS

Staff Emeritus
I needed to read that more closely ...

6. Apr 7, 2014

### vela

Staff Emeritus
I didn't word it very well. I changed the wording so it's a bit clearer.

7. Apr 7, 2014

### az_lender

The derivatives of both arctan(x) and arctanh(x) have x^2 in their denominators, so I can't agree with your initial result. But note the identity sqrt[cosh(z) + 1] = 2 cosh(z/2), which will help you get a correct answer for the original integral.

A further point: please don't write an integral without a differential, it's meaningless. Thus, one does not EVER integrate 1/[cosh(z)+1], rather one integrates dz/[cosh(z)+1].