Could someone explain how to do this question? I dont fully understand how you could use hyperbolic functions to show the function..
Is this for the purposes of integration?
$\displaystyle \frac{x^4 - 1}{x^4 + 1} = \frac{x^4 + 1 - 2}{x^4 + 1}$
$\displaystyle = \frac{x^4 + 1}{x^4 + 1} - \frac{2}{x^4 - 1}$
$\displaystyle = 1 - \frac{2}{x^4 - 1}$.
Now use partial fractions on the second term. You will need to use the Partial Fractions method twice.
Once you have done this, when you integrate, you will have one term that involves a logarithm and one term that involves a trigonometric/hyperbolic substitution.