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Popular >

integral of x^2(x-6)

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

Popular Examples

integral from 0 to 2pi of sin^2(15x)

\int_{0}^{2 π} sin^{2} (15 x) d x

limit as x approaches 4 of (x^2+16-64)/x

x \to 4 lim (\frac{x ^{2} + 16 - 64}{x})

sum from n=0 to infinity of ((1/3)^n)^2

n = 0 \sum \infty ((\frac{1}{3})^{n})^{2}

derivative of 6sin(2pix)

\frac{d}{d x} (6 sin (2 π x))

integral of 8cos(θ)sin(θ)

\int 8 cos (θ) sin (θ) d θ

Frequently Asked Questions (FAQ)

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