Question

Find the value of
I = integral of ((4arcsin(x))/sqrt(1-x^2))

Answer 1

\[I = \int\limits_{0}^{1/2} \frac{ 4\sin^{-1} x }{ \sqrt{1-x^2} }\]

Answer 2

Try a substitution. If I recall correctly, the derivative of arcsine gives you the expression in the denominator.

Answer 3

It worked thanks a lot!