Solving a Nasty Integral: Any Ideas?

[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,

 

[Pere Callahan]

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

 

[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.

 

[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.

 

[Big-T]

Sech(x) is not Sec(H(x)), but the secant hyperbolicus function.
See: http://mathworld.wolfram.com/HyperbolicSecant.html

 

[racer]

Sech(x) is not Sec(H(x)), but the secant hyperbolicus function.
See: http://mathworld.wolfram.com/HyperbolicSecant.html

I am sorry.