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Popular >

integral of-x^2+x

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (2-3e^y)

\int (2 - 3 e^{y}) d y

integral of x^3arccos(x)

\int x^{3} arccos (x) d x

integral of 2x^3 integral

2 x^{3}

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

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

integral of (e^x)/(\sqrt[3]{1+e^x)}

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

Frequently Asked Questions (FAQ)

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