How to compute $\int \sqrt{\frac{x^2-3}{x^{11}}}dx$ How to compute the following integral ??
$\displaystyle\int \sqrt{\frac{x^2-3}{x^{11}}}dx$
I use the wolfram Alpha to get an ugly answer
http://www.wolframalpha.com/input/?i=integral++%28%28x^2-3%29%2Fx^%2811%29%29^0.5+dx
But there is no step for me

If you are looking for a simple expression it does not exists. You integral has the form
$$
\int (x^2-3)^{\frac{1}{2}}x^{-\frac{11}{2}} dx
$$
The expression of the form
$$
\int (a+bx^n)^px^m dx
$$
is called a differential binomial and can be integrated in elementary functions only if $p$ is an integer (not), $(m+1)/n$ is an integer (not), or $p+(m+1)/n$ (not).
Added You can use the substitutions $x=t^\alpha$, where $\alpha$ is the common denominator of $m$ and $n$; $a+bx^n=t^{\alpha}$ where $\alpha$ is the denominator of $p$; $ax^{-n}+b=t^\alpha$, where $\alpha$ is the denominator of $p$ correspondingly. 
