What is the integral of x^3-x^2-14x ?

The integral of x^3-x^2-14x is (x^4)/4-(x^3)/3-7x^2+C

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integral of x^3-x^2-14x

\int x^{3} - x^{2} - 14 x d x

\frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 7 x^{2} + C

Solution steps

\int x^{3} - x^{2} - 14 x 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 x^{3} d x - \int x^{2} d x - \int 14 x d x

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

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

\int 14 x d x = 7 x^{2}

= \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 7 x^{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 7 x^{2} + C

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What is the integral of x^3-x^2-14x ?
The integral of x^3-x^2-14x is (x^4)/4-(x^3)/3-7x^2+C