What is the integral of x(x-1)(3-x) ?

The integral of x(x-1)(3-x) is (4x^3)/3-(x^4)/4-(3x^2)/2+C

Popular >

integral of x(x-1)(3-x)

\int x (x - 1) (3 - x) d x

\frac{4 x ^{3}}{3} - \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2} + C

Solution steps

\int x (x - 1) (3 - x) d x

Expand

x (x - 1) (3 - x) : 4 x^{2} - x^{3} - 3 x

= \int 4 x^{2} - x^{3} - 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 4 x^{2} d x - \int x^{3} d x - \int 3 x d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int x^{3} d x = \frac{x ^{4}}{4}

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

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{4 x ^{3}}{3} - \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2} + C

\int_{2}^{3} \frac{x}{x ^{2} - 1} d x

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{4}})

\int \frac{e ^{6 x}}{e ^{12 x} + 49} d x

\frac{\partial}{\partial x} (sin (z))

What is the integral of x(x-1)(3-x) ?
The integral of x(x-1)(3-x) is (4x^3)/3-(x^4)/4-(3x^2)/2+C