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Popular >

integral of (1-x)x

Solution

\int (1 - x) x d x

Solution

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

Solution steps

\int (1 - x) x d x

Expand

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

= \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 ((3x^2))/(x^3+4)

\int \frac{( 3 x ^{2} )}{x ^{3} + 4} d x

integral of 4xsin(4x^2)

\int 4 x sin (4 x^{2}) d x

integral of x/(y^2+x^2)

\int \frac{x}{y ^{2} + x ^{2}} d y

integral of e^{-3x}*x

\int e^{- 3 x} \cdot x d x

integral of cos(x)(1-sin^2(x))

\int cos (x) (1 - sin^{2} (x)) d x

Frequently Asked Questions (FAQ)

What is the integral of (1-x)x ?
The integral of (1-x)x is (x^2)/2-(x^3)/3+C