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Popular >

integral of x^2(6-x)

Solution

\int x^{2} (6 - x) d x

Solution

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

Solution steps

\int x^{2} (6 - x) d x

Expand

x^{2} (6 - x) : 6 x^{2} - x^{3}

= \int 6 x^{2} - x^{3} 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 6 x^{2} d x - \int x^{3} d x

\int 6 x^{2} d x = 2 x^{3}

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

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

Add a constant to the solution

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

Popular Examples

2y^{''}-y^'-y=6e^{-x/2}

2 y^{^{''}} - y^{^{'}} - y = 6 e^{- \frac{x}{2}}

derivative of 7/(sqrt(x+5))

\frac{d}{d x} (\frac{7}{x + 5})

derivative of sin(4x+3)

\frac{d}{d x} (sin (4 x + 3))

y^'=((x+y)^2)/(2x^2)

y^{^{'}} = \frac{( x + y ) ^{2}}{2 x ^{2}}

tangent of f(x)=3x^3+2x^2+1,\at x=-1 tangent of

f (x) = 3 x^{3} + 2 x^{2} + 1, at x = - 1

Frequently Asked Questions (FAQ)

What is the integral of x^2(6-x) ?
The integral of x^2(6-x) is 2x^3-(x^4)/4+C