integrate arcsin(x)

Use integration by parts to obtain:u=arcsin(x), u'=1/(1-x²)^0.5, and v'=1, v=x
Using the equation: integral of uv' = uv - integral of u'vintegral of arcsin(x) = xarcsin(x) - integral of x/(1-x²)^0.5
Use integration by substitution to obtain to integrate x/(1-x²)^0.5:u=1-x², du/dx=-2x, dx=-du/2xThe integral becomes: -1/2u^0.5Solving using the power rules, the solution is: -u^0.5Solving back using x: -(1-x²)^0.5
Thus, the final solution becomes: xarcsin(x)+(1-x2)0.5+c