What is the integral of (288)/((2x-4)^2) ?

The integral of (288)/((2x-4)^2) is -(72)/(x-2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (288)/((2x-4)^2)

\int \frac{288}{( 2 x - 4 ) ^{2}} d x

- \frac{72}{x - 2} + C

Solution steps

\int \frac{288}{( 2 x - 4 ) ^{2}} d x

Take the constant out:

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

= 288 \cdot \int \frac{1}{( 2 x - 4 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{2 u ^{2}} d u

= 288 \cdot \int \frac{1}{2 u ^{2}} d u

Take the constant out:

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

= 288 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 288 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = 2 x - 4

= 288 \cdot \frac{1}{2} (- \frac{1}{2 x - 4})

Simplify

288 \cdot \frac{1}{2} (- \frac{1}{2 x - 4}) : - \frac{72}{x - 2}

= - \frac{72}{x - 2}

Add a constant to the solution

= - \frac{72}{x - 2} + C

f (x) = 6 x - 12, [1, 5]

x \to \infty lim (sin (x))

f (x) = 4 sec (x) + tan (x)

\int x e^{- 0.5 x} d x

n = 1 \sum \infty n e^{- 3 n^{2}}

What is the integral of (288)/((2x-4)^2) ?
The integral of (288)/((2x-4)^2) is -(72)/(x-2)+C