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 2166 views around the world You can reuse this answer Creative Commons License