How do you integrate #int x^3cos(x^2)# using integration by parts? Calculus Techniques of Integration Integration by Parts 1 Answer Eddie Aug 28, 2016 #= 1/2 x^2 sin(x^2) + 1/2cos(x^2) + C# Explanation: #int x^3cos(x^2)# #int x^2 . x cos(x^2)# #= int x^2 d/dx (1/2 sin(x^2))# ready for IBP #= 1/2 x^2 sin(x^2) - 1/2 int d/dx (x^2) sin(x^2)# #= 1/2 x^2 sin(x^2) - int x sin(x^2)# #= 1/2 x^2 sin(x^2) - int d/dx ( - 1/2cos(x^2))# #= 1/2 x^2 sin(x^2) + 1/2cos(x^2) + C# Answer link Related questions How do I find the integral #int(x*ln(x))dx# ? How do I find the integral #int(cos(x)/e^x)dx# ? How do I find the integral #int(x*cos(5x))dx# ? How do I find the integral #int(x*e^-x)dx# ? How do I find the integral #int(x^2*sin(pix))dx# ? How do I find the integral #intln(2x+1)dx# ? How do I find the integral #intsin^-1(x)dx# ? How do I find the integral #intarctan(4x)dx# ? How do I find the integral #intx^5*ln(x)dx# ? How do I find the integral #intx*2^xdx# ? See all questions in Integration by Parts Impact of this question 2427 views around the world You can reuse this answer Creative Commons License