Integral involving a power of the Arcsin: Find.

Since a power of the Arcsin is present in the integrand, we may be able to apply the Power Rule for Integration. To check this, substitute w for the Arcsin:

Let . Using the Derivative of the Arcsin, we get

, or . Now we substitute these results into the original equation:

. Next apply the Power Rule of Integration:

. Finally, we convert back to a function of x by replacing w: