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

The integral of x^3(x^2-2x) is (x^6)/6-(2x^5)/5+C

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

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

\frac{x ^{6}}{6} - \frac{2 x ^{5}}{5} + C

Solution steps

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

Expand

x^{3} (x^{2} - 2 x) : x^{5} - 2 x^{4}

= \int x^{5} - 2 x^{4} 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^{5} d x - \int 2 x^{4} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

= \frac{x ^{6}}{6} - \frac{2 x ^{5}}{5}

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{2 x ^{5}}{5} + C

\frac{d}{d x} ((5 x^{2} - 4 x) e^{x})

3 x e^{\frac{- 1}{y ^{3}}}

\int cos^{6} (x) sin (x) d x

y = 11 + cot^{2} (x)

\frac{d}{d x} (I n (x))

What is the integral of x^3(x^2-2x) ?
The integral of x^3(x^2-2x) is (x^6)/6-(2x^5)/5+C