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Popular >

integral of x(3-x)

Solution

\int x (3 - x) d x

Solution

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

Solution steps

\int x (3 - x) d x

Expand

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

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

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

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (5e^x)/(e^{2x)+6e^x+9}

\int \frac{5 e ^{x}}{e ^{2 x} + 6 e ^{x} + 9} d x

integral from 0 to 2 of (4x-x^3)

\int_{0}^{2} (4 x - x^{3}) d x

inverse oflaplace ((4s-3))/((s^2+8s+24))inverse laplace

\frac{( 4 s - 3 )}{( s ^{2} + 8 s + 24 )}

area x+2y=7,x+8=y^2 area

x + 2 y = 7, x + 8 = y^{2}

integral of 14x^6y^{-4}-12x^5y^{-3}

\int 14 x^{6} y^{- 4} - 12 x^{5} y^{- 3} d x

Frequently Asked Questions (FAQ)

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