sin y d y Solution Let u =arcsin(x) du = dx/(1 - x²) dv =dx v = x udv = uv - vdu arcsin(x) dx = x arcsin(x) - x dx /(1- x²) The last integral can be solved by a simple substitution: let z = (1 - x²) dz = -2x dx dz/2 = - x dx 1/2 dz/u = 1/2 z^(-1/2) dz = 1/2 * 2 z^(1/2) = z^(1/2) = (1 - x²) Final integral is: x arcsin(x) + (1 + x²) + C.