How do you integrate #int (x^3-4x+2)dx#? Calculus Introduction to Integration Integrals of Polynomial functions 1 Answer Ratnaker Mehta Feb 5, 2017 #x^4/4-2x^2+2x+C.# Explanation: Recall that #intx^ndx=x^(n+1)/(n+1)+c_1, n!=-1,#and, for a constant #k#, #int[kf(x)+-g(x)]dx=kintf(x)dx+-intg(x)dx+c_2.# Hence, the reqd. Integral#=intx^3dx-4intx^1dx+2intx^0dx# #=x^(3+1)/(3+1)-4(x^2/2)+2x# #=x^4/4-2x^2+2x+C.# 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 5053 views around the world You can reuse this answer Creative Commons License