I am trying to find $\int \frac {dx}{x^2 \sqrt{4-x^2}}$
I make $t=2\sin x$
$\int \frac {dx}{x^2 \sqrt{4-4\sin^2 t}}$
$\int \frac {dx}{x^2 \sqrt{4(1-\sin^2 t)}}$
$\int \frac {dx}{x^2 \sqrt{4(\cos^2 t)}}$
$\int \frac {dx}{x^2 \cdot 2\cos t}$
I do not really know where to go from here. I have two variables and that is really bad but I do not know how to write $x$ in terms of $t$.