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Popular >

integral of x(x-4)

Solution

\int x (x - 4) d x

Solution

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

Solution steps

\int x (x - 4) d x

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral of 1/(sqrt(e^{2x-1))}

\int \frac{1}{e ^{2 x - 1}} d x

(\partial}{\partial x}(\frac{y^2)/x)

\frac{\partial}{\partial x} (\frac{y ^{2}}{x})

integral of (7x^3-7x+5)/(x^3-x^2)

\int \frac{7 x ^{3} - 7 x + 5}{x ^{3} - x ^{2}} d x

derivative of (20/x)

\frac{d}{d x} (\frac{20}{x})

limit as x approaches m+of x-[x]

x \to m + lim (x - [x])

Frequently Asked Questions (FAQ)

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