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Popular >

integral of x(-x)

Solution

\int x (- x) d x

Solution

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

Solution steps

\int x (- x) d x

Simplify

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

= \int - x^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

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

Add a constant to the solution

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

Popular Examples

integral of (4x^3+5)sqrt(x^4+5x)

\int (4 x^{3} + 5) x^{4} + 5 x d x

integral of (1-e)

\int (1 - e) d x

integral of (3x)/(x-2)

\int \frac{3 x}{x - 2} d x

integral of (sin(x)+cos(x))^3

\int (sin (x) + cos (x))^{3} d x

integral of (x^3)ln(x)(1)

\int (x^{3}) ln (x) (1) d x

Frequently Asked Questions (FAQ)

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