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.