Hey. I was reviewing some trig substitution and I know how to solve the problem but I was curious if you can also solve it by using two different substitutions/change of varaibles? If so, how would you relate the functions? Consider for example: ∫ (1-x^2)^1/2 dx, -1<= x <= 1 x = sin Θ dx = cos Θ dΘ -pi/2 <= Θ <= pi/2 ∫ (1-x^2)^1/2 dx = ∫ 1 - sin^2Θ dΘ u = 2Θ du = 2 dΘ -pi <= u <= pi Then the integral is equal to: Θ - 1/2Θ - 1/2 sin u(Θ(x)) + C where Θ(x) = sin^-1x. Would u(Θ(x)) = 2arcsinx be true? Which would give us: arcsin x - 1/2arcsin x - 1/2 sin (2arcsin x) + C However ugly it is, would this be correct with the adjusted interval? Does it make sense?