Integrate w/negative exponent

I need a little 'suggestion' as to how to integrate cos^6x sin^-3x dx.

I rewrite to cos^6x/sin^3x dx and let u = sinx but when I'm trying to rewrite integral, what should I do with the ^6?

Thanks!

$$\int \frac{cos^6 t}{sin^3 t}dt= \frac{cos ^6 t sin t}{sin^4 t}dt$$
$$= \int \frac{cos^6 t}{(1- cos^2 t)^2}(sin t dt)$$
$$-\int\frac{x^6}{(1-x^2)^2}dx$$