# A Nasty integral

1. Apr 22, 2008

### WalkingInMud

Any Ideas on how to Approach this one? ...

$$\int\sqrt{[1-sech(u)]^{2}+ [-tanh(u)sech(u)]^{2}}du$$

We have a $$sech(u)$$ and its derivative $$-tanh(u)sech(u)$$ and this suggests some sort of substitution maybe, but the radical makes it a bit nasty for Me.

Any Ideas? ...Thanks Heaps,

2. Apr 22, 2008

### Pere Callahan

Why would you think there exists a primitive which can be expressed as a combinaton of "simple" function?

3. Apr 24, 2008

### grmnsplx

I doubt this will have a pretty substitution
Maybe use the generalized binomial expansion...

If that works you'll probably get a hypergeometric solution.

4. Apr 25, 2008

### racer

Hello there

I am not sure but I have few ideas and they might help.

[1-secH(X)]^2 becomes -tanH(X)

[cosX]^2 + [SinX]^2 = 1

Dvide by [cosX]^2 and you will have

1+[TanX]^2 = 1 over CosX^2 which [SecX]^2
1- [SecX]^2 = -[tanX]^2

The root of the first one is -[tanX] if I am not mistaken.
The Second one becomes [-SecH(x)]^2

This works if H is not a constant.

5. Apr 25, 2008

### Big-T

6. Apr 25, 2008