What is the integral of (5x^3-8x^2) ?

The integral of (5x^3-8x^2) is (5x^4)/4-(8x^3)/3+C

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integral of (5x^3-8x^2)

\int (5 x^{3} - 8 x^{2}) d x

\frac{5 x ^{4}}{4} - \frac{8 x ^{3}}{3} + C

Solution steps

\int 5 x^{3} - 8 x^{2} 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 5 x^{3} d x - \int 8 x^{2} d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 8 x^{2} d x = \frac{8 x ^{3}}{3}

= \frac{5 x ^{4}}{4} - \frac{8 x ^{3}}{3}

Add a constant to the solution

= \frac{5 x ^{4}}{4} - \frac{8 x ^{3}}{3} + C

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What is the integral of (5x^3-8x^2) ?
The integral of (5x^3-8x^2) is (5x^4)/4-(8x^3)/3+C