en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x-4)^2

Solution

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

Solution

\frac{x ^{3}}{3} - 4 x^{2} + 16 x + C

Solution steps

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

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int x^{2} - 8 x + 16 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^{2} d x - \int 8 x d x + \int 16 d x

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

\int 8 x d x = 4 x^{2}

\int 16 d x = 16 x

= \frac{x ^{3}}{3} - 4 x^{2} + 16 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 4 x^{2} + 16 x + C

Popular Examples

limit as x approaches 0+of (x+1)^{Inx}

x \to 0 + lim ((x + 1)^{I n x})

integral of ((ln(x)))/(x^3)

\int \frac{( ln ( x ) )}{x ^{3}} d x

\frac{d v}{d t} = - k v

(dy}{dx}-(7y)/x =\frac{y^3)/(x^9)

\frac{d y}{d x} - \frac{7 y}{x} = \frac{y ^{3}}{x ^{9}}

derivative of (3x^2/(2x+1))

\frac{d}{d x} (\frac{3 x ^{2}}{2 x + 1})

Frequently Asked Questions (FAQ)

What is the integral of (x-4)^2 ?
The integral of (x-4)^2 is (x^3)/3-4x^2+16x+C