Use integration by parts to find .

Answer

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

Then

We put everything in the formula and get

Thankfully, we can use substitution to find this new integral.