en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 3x(x-4)

Solution

\int 3 x (x - 4) d x

Solution

x^{3} - 6 x^{2} + C

Solution steps

\int 3 x (x - 4) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x (x - 4) d x

Expand

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

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

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

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

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

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

Simplify

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

= x^{3} - 6 x^{2}

Add a constant to the solution

= x^{3} - 6 x^{2} + C

Graph

Popular Examples

derivative of x^2{z}(x)

limit as x approaches e of x^2*e^{x^2}

derivative of f(x)=2e^x*(x^2+3x-9)^2

d/(dθ)((cos(θ))/(sin(θ)))

derivative of 2^{4x}

Frequently Asked Questions (FAQ)

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