en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-4)^2

Solution

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

Solution

\frac{4 x ^{3}}{3} - 8 x^{2} + 16 x + C

Solution steps

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

Expand

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

= \int 4 x^{2} - 16 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 4 x^{2} d x - \int 16 x d x + \int 16 d x

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

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

\int 16 d x = 16 x

= \frac{4 x ^{3}}{3} - 8 x^{2} + 16 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} - 8 x^{2} + 16 x + C

Popular Examples

y^{''}+4y=x-1/20 x^2

y^{^{''}} + 4 y = x - \frac{1}{20} x^{2}

derivative of t^3-12t^2+36t derivative of

t^{3} - 12 t^{2} + 36 t

(\partial)/(\partial x)(cos(bx+c)e^{xy}x)

\frac{\partial}{\partial x} (cos (b x + c) e^{x y} x)

derivative of 18cos(x)+9sin^2(x)derivative of

18 cos (x) + 9 sin^{2} (x)

integral of-cos(u)

\int - cos (u) d u

Frequently Asked Questions (FAQ)

What is the integral of (2x-4)^2 ?
The integral of (2x-4)^2 is (4x^3)/3-8x^2+16x+C