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Popular >

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

Popular Examples

integral of (-2/x)

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

integral of 1/(sqrt((2x-x^2)^3))

\int \frac{1}{( 2 x - x ^{2} ) ^{3}} d x

integral of x^3e^{x^4+1}

\int x^{3} e^{x^{4} + 1} d x

integral of (9x^2+x)/((12x^3+2x^2)^2)

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

integral of (5e^{-1/x})/(x^2)

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