The calculator will find the integral/antiderivative of
x3−3x2, with steps shown.
Related calculator:
Definite and Improper Integral Calculator
Solution
Integrate term by term:
∫(x3−3x2)dx=(−∫3x2dx+∫x3dx)
Apply the power rule ∫xndx=n+1xn+1 (n=−1) with n=3:
−∫3x2dx+∫x3dx=−∫3x2dx+1+3x1+3=−∫3x2dx+(4x4)
Apply the constant multiple rule ∫cf(x)dx=c∫f(x)dx with c=3 and f(x)=x2:
4x4−∫3x2dx=4x4−(3∫x2dx)
Apply the power rule ∫xndx=n+1xn+1 (n=−1) with n=2:
4x4−3∫x2dx=4x4−31+2x1+2=4x4−3(3x3)
Therefore,
∫(x3−3x2)dx=4x4−x3
Simplify:
∫(x3−3x2)dx=4x3(x−4)
Add the constant of integration:
∫(x3−3x2)dx=4x3(x−4)+C
Answer: ∫(x3−3x2)dx=4x3(x−4)+C