$\displaystyle

\int {\frac{{dx}}

{{(x^2 - 1)^2 }}} = \int {\frac{{dx}}

{{(x - 1)^2 (x + 1)^2 }}}

$

It seems no matter what I try after this I cannot get the answer in the book.

Which is:

$\displaystyle

\frac{1}

{4}\int {(\frac{{ - 1}}

{{x - 1}}} + \frac{1}

{{(x - 1)^2 }} + \frac{1}

{{x + 1}} + \frac{1}

{{(x + 1)^2 }})dx

$

Any help would be greatly appreciated.