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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

Popular Examples

integral of cot^3(2x)csc(2x)

\int cot^{3} (2 x) csc (2 x) d x

integral of x^2arctan(x/2)

\int x^{2} arctan (\frac{x}{2}) d x

integral of (sqrt(x+1))/(x+2)

\int \frac{x + 1}{x + 2} d x

integral of x^2\sqrt[3]{1+x^3}

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

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

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