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Popular Calculus >

integral of x-2x^2

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

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\int (- \frac{2}{x}) d x

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\int \frac{9 x ^{2} + x}{( 12 x ^{3} + 2 x ^{2} ) ^{2}} d x

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\int \frac{5 e ^{- \frac{1}{x}}}{x ^{2}} d x

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\int (2 x - 1) \cdot ln (x) d x

integral of x\sqrt[4]{1-3x^2}

\int x 4 1 - 3 x^{2} d x

Frequently Asked Questions (FAQ)

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