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Popular >

integral of (2x-x^2)

Solution

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

Solution

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

Solution steps

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

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

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

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

Add a constant to the solution

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

Popular Examples

limit as x approaches 0 of [x^2]-[x^3]

x \to 0 lim ([x^{2}] - [x^{3}])

derivative of (-1^x)

\frac{d}{d x} ((- 1)^{x})

integral of x^2e^{x+4}

\int x^{2} e^{x + 4} d x

integral of 1+1/y

\int 1 + \frac{1}{y} d y

integral of (3x)/((4-x^2)^3)

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

Frequently Asked Questions (FAQ)

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