I am having a problem solving an integral. I am stuck in an infinite loop. Integral is:
$\int{\frac{dx}{\sqrt{1-x^2}\arcsin{x}}}$
I have separated it in dv and u on this way:
$u = \frac{dx}{\sqrt{1-x^2}}$ $dv = \frac{1}{\arcsin{x}}$
And the using:
$u v - \int{v \, du}$
I get again:
$\int{\frac{dx}{\sqrt{1-x^2}\arcsin{x}}}$
I dont know, but probably, I am doing something wrong. I am new at solving Integrals so I am learning :) According to my book the result should be:
$\ln({\arcsin{x}})-C$
And it will be true if I didn't had $\sqrt{1-x^2}$ but on this way I have no idea.