Can`t find the integral $\int\frac{dx}{\sqrt x\sin(x)}$ $\int\frac{dx}{\sqrt x\sin(x)}$ Im stuck in this problem for about 40 minutes. Any clue how to solve this?
The actual problem is an ODE problem, it is given $x^2y''+xy'+(x^2-1/4)y=0$ and one of the solutions is $y_1(x)=\sin(x)/\sqrt(x)$. So I need to find $v=\int{\frac{e^{-\int{p(x)\,dx}}}{\sin(x)/\sqrt(x)}}\,dx$.

The solution you have suggests that you let
$$
y(x)=v(x)/\sqrt{x}.
$$
Doing so, your differential equation will turn into
$$
x^{3/2}(v''(x)+v(x))=0.
$$
I'm sure you can take it from there.
(I don't see where you got your integral from, so I cannot help you with that.)
