Originally I had this integrand:

$\displaystyle \int \frac{dx}{x^4\sqrt{x^2+3}}$

http://www.wolframalpha.com/input/?i...8x^2%2B3%29%29

I don't understand how the software came up with $\displaystyle \frac {1}{9}cot^3(u)*csc(u)$

When I simplified it the same way it did I came up with

$\displaystyle \frac{sec(u)}{9tan^4(u)}$

How did wolframalpha simplify it? Or did I just simplify it incorrectly?