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Popular >

integral of x(x+3)

Solution

\int x (x + 3) d x

Solution

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

Solution steps

\int x (x + 3) d x

Expand

x (x + 3) : x^{2} + 3 x

= \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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integral of 2te^{-t^2}

\int 2 t e^{- t^{2}} d t

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\int_{0}^{1} x 1 - x^{2} d x

integral of (2u-1)/(-u+2)

\int \frac{2 u - 1}{- u + 2} d u

derivative of ((x+1^2)/(x+3))

\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{x + 3})

Frequently Asked Questions (FAQ)

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