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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

\int_{0}^{1} x e^{x^{2}} - e^{x} d x

\int_{0}^{π} cos^{4} (x) d x

\frac{y ^{^{'}}}{x} = 2 x^{2} - y

f (x) = - \frac{4 x}{( x - 2 ) ^{3}}

g (t) = 5 - x

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