How do you integrate # (1-x^2)^.5#? Calculus Techniques of Integration Integration by Substitution 1 Answer Eddie Jul 4, 2016 #= 1/2 x sqrt(1-x^2) + arcsin x/2 + C # Explanation: #int dx qquad sqrt(1-x^2)# trig sub #x = sin phi, dx = cos phi dphi# #implies int dphi qquad cos phi sqrt(1-sin^2 phi)# #= int dphi qquad cos^2 phi # double angle # cos 2A = 2 cos^2 A - 1# #= int dphi qquad (cos 2 phi + 1)/2 # #= 1/4 sin 2 phi + phi/2 + C # double angle #sin 2A = 2 sin A cos A# #= 1/2 x sqrt(1-x^2) + arcsin x/2 + C # Answer link Related questions What is Integration by Substitution? How is integration by substitution related to the chain rule? How do you know When to use integration by substitution? How do you use Integration by Substitution to find #intx^2*sqrt(x^3+1)dx#? How do you use Integration by Substitution to find #intdx/(1-6x)^4dx#? How do you use Integration by Substitution to find #intcos^3(x)*sin(x)dx#? How do you use Integration by Substitution to find #intx*sin(x^2)dx#? How do you use Integration by Substitution to find #intdx/(5-3x)#? How do you use Integration by Substitution to find #intx/(x^2+1)dx#? How do you use Integration by Substitution to find #inte^x*cos(e^x)dx#? See all questions in Integration by Substitution Impact of this question 1174 views around the world You can reuse this answer Creative Commons License