How to integrate $\int \frac{1}{\sin^4(x)\cos^4(x)}\,\mathrm dx$? How can I integrate $$\int \frac{1}{\sin^4(x)\cos^4(x)}\,\mathrm dx.$$
So I know that for this one we have to use a trigonometric identity or a substitution. Integration by parts is probably not going to help. Can someone please point out what should I do to evaluate this integral?  
Thanks!

All integrals of rational functions of $sin(x)$ and $cos(x)$ can be solved by rationally parameterizing the unit circle ( see http://mathnow.wordpress.com/2009/11/06/a-rational-parameterization-of-the-unit-circle/  for example). This will convert the integral into a rational integral, which are all solvable by partial fraction decomposition.  Try this out for the infamous $\int sec^3(x)dx$ for instance.
