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Popular >

integral of-x^2+3x

Solution

\int - x^{2} + 3 x d x

Solution

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

Solution steps

\int - x^{2} + 3 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 3 x d x

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

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

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

Add a constant to the solution

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

Popular Examples

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\frac{d y}{d x} - \frac{y}{x} = 5 x e^{x}

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\int \frac{2}{- sin ( t ) + 1} d t

derivative of 1/(log_{e(x)})

\frac{d}{d x} (\frac{1}{lo g _{e} ( x )})

Frequently Asked Questions (FAQ)

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