What is the integral of (900)/((2x-5)^2) ?

The integral of (900)/((2x-5)^2) is -(450)/(2x-5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (900)/((2x-5)^2)

\int \frac{900}{( 2 x - 5 ) ^{2}} d x

- \frac{450}{2 x - 5} + C

Solution steps

\int \frac{900}{( 2 x - 5 ) ^{2}} d x

Take the constant out:

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

= 900 \cdot \int \frac{1}{( 2 x - 5 ) ^{2}} d x

Apply u-substitution

= 900 \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

= 900 \cdot \frac{1}{2} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

= 900 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = 2 x - 5

= 900 \cdot \frac{1}{2} (- \frac{1}{2 x - 5})

Simplify

900 \cdot \frac{1}{2} (- \frac{1}{2 x - 5}) : - \frac{450}{2 x - 5}

= - \frac{450}{2 x - 5}

Add a constant to the solution

= - \frac{450}{2 x - 5} + C

What is the integral of (900)/((2x-5)^2) ?
The integral of (900)/((2x-5)^2) is -(450)/(2x-5)+C