How to integrate this integral? I had a problem with this specific integral:
$$
\int{\sqrt{\frac{x^3 -3}{x^{11}}} \ dx}
$$
Thank you ahead of time.

$$ \int \sqrt{\frac{x^3-3}{x^{11}}}\,dx = \int \frac{1}{x^4} \sqrt{\frac{x^3-3}{x^3}} \,dx 
= \int \frac{1}{x^4} \sqrt{1-\frac{3}{x^3}} \,dx $$
Let 
$$ u = \frac{1}{x^3}, \; du = -\frac{3}{x^4} dx $$
The above integral becomes
$$ -\frac{1}{3} \int \sqrt{1-3u}\:du = -\frac{1}{3} \cdot -\frac{1}{3} \cdot \frac{2}{3} 
(1-3u)^{3/2} + C = \frac{2}{27} \left(1 - \frac{3}{x^3}\right)^{3/2} + C $$
