Use integration by parts to find .
It might be useful to remember that the derivative of arcsin x is
We can rewrite the integrand to show the factor of 1 that's already there:
We can't choose v' = arcsin x, because if we knew the antiderivative of arcsin x we'd already be done with this problem. So take
u = arcsin x
v' = 1
We put everything in the formula and get
Thankfully, we can use substitution to find this new integral.