What is the integral of 4x^2-2x^3 ?

The integral of 4x^2-2x^3 is (4x^3)/3-(x^4)/2+C

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integral of 4x^2-2x^3

\int 4 x^{2} - 2 x^{3} d x

\frac{4 x ^{3}}{3} - \frac{x ^{4}}{2} + C

Solution steps

\int 4 x^{2} - 2 x^{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x^{2} d x - \int 2 x^{3} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 2 x^{3} d x = \frac{x ^{4}}{2}

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{2}

Add a constant to the solution

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{2} + C

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What is the integral of 4x^2-2x^3 ?
The integral of 4x^2-2x^3 is (4x^3)/3-(x^4)/2+C