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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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