What is the general antiderivative of #f(x) = x(4 − x)^2#? Calculus Introduction to Integration Integrals of Polynomial functions 1 Answer vince · MeneerNask Feb 23, 2015 Hello, Because #f(x) = x(16 - 8x + x^2) = x^3 - 8x^2 + 16x#, so any antiderivative of #f# is #F(x) = (x^4)/4 - 8/3 x^3 + 8x^2 + c# where #c# is an arbitrary real constant. Answer link Related questions How do you evaluate the integral #intx^3+4x^2+5 dx#? How do you evaluate the integral #int(1+x)^2 dx#? How do you evaluate the integral #int8x+3 dx#? How do you evaluate the integral #intx^10-6x^5+2x^3 dx#? What is the integral of a constant? What is the antiderivative of the distance function? What is the integral of #|x|#? What is the integral of #3x#? What is the integral of #4x^3#? What is the integral of #sqrt(1-x^2)#? See all questions in Integrals of Polynomial functions Impact of this question 2098 views around the world You can reuse this answer Creative Commons License