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Popular >

integral of x-x^2

Solution

\int x - x^{2} d x

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

derivative of (-4x^6+4x^5-3x^3/(3x^2))

\frac{d}{d x} (\frac{- 4 x ^{6} + 4 x ^{5} - 3 x ^{3}}{3 x ^{2}})

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\frac{50}{x}

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\int \frac{20}{1 - cos ( 4 x )} d x

limit as x approaches 4 of (x+5)/(x-4)

x \to 4 lim (\frac{x + 5}{x - 4})

Frequently Asked Questions (FAQ)

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