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## Homework Statement

Sorry for the poor use of Latex, I have tried to get it to work but it seems to never come out as I would like.

Using a trigonometric or hyperbolic substitution, evaluate the following indfenite integral,

∫[itex]\frac{1}{\sqrt{(x^2-1)^5}}[/itex] dx

## Homework Equations

I have got down to a point where I am stuck and was wondering which path to go down next.

## The Attempt at a Solution

let x=cosh[itex]\phi[/itex]

dx/d[itex]\phi[/itex]=sinh[itex]\phi[/itex]

dx=sinh[itex]\phi[/itex] d[itex]\phi[/itex]

Then (x

^{2}-1) = cosh

^{2}[itex]\phi[/itex]-1

= sinh

^{2}[itex]\phi[/itex]

(x

^{2}-1)

^{1/2}= sinh[itex]\phi[/itex]

(x

^{2}-1)

^{5/2}= sinh

^{5}[itex]\phi[/itex]

therefore ∫sinh[itex]\phi[/itex]/sinh

^{5}[itex]\phi[/itex]

=∫1/sinh

^{4}[itex]\phi[/itex]

=∫cosec

^{2}[itex]\phi[/itex]

Is this right so far, Do i then split the (cosec[itex]\phi[/itex])^4 into two and do the integral then.?