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Popular >

integral of x(x-2)

Solution

\int x (x - 2) d x

Solution

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

Solution steps

\int x (x - 2) d x

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

derivative of ((4x^2+8x+4))/(sqrt(x))derivative of

\frac{( 4 x ^{2} + 8 x + 4 )}{x}

integral of x^3e^{2x^4}

\int x^{3} e^{2 x^{4}} d x

tangent of y=e^x(x^2-3)tangent of

y = e^{x} (x^{2} - 3)

integral of sin(8pit)

\int sin (8 π t) d t

derivative of xln(2x+3)

\frac{d}{d x} (x ln (2 x + 3))

Frequently Asked Questions (FAQ)

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