What is the integral of (300)/((3x+25)^2) ?

The integral of (300)/((3x+25)^2) is -(100)/(3x+25)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (300)/((3x+25)^2)

\int \frac{300}{( 3 x + 25 ) ^{2}} d x

- \frac{100}{3 x + 25} + C

Solution steps

\int \frac{300}{( 3 x + 25 ) ^{2}} d x

Take the constant out:

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

= 300 \cdot \int \frac{1}{( 3 x + 25 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{3 u ^{2}} d u

= 300 \cdot \int \frac{1}{3 u ^{2}} d u

Take the constant out:

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

= 300 \cdot \frac{1}{3} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 300 \cdot \frac{1}{3} (- \frac{1}{u})

Substitute back

u = 3 x + 25

= 300 \cdot \frac{1}{3} (- \frac{1}{3 x + 25})

Simplify

300 \cdot \frac{1}{3} (- \frac{1}{3 x + 25}) : - \frac{100}{3 x + 25}

= - \frac{100}{3 x + 25}

Add a constant to the solution

= - \frac{100}{3 x + 25} + C

\int \frac{1}{( x + 1 ) ( x ^{2} + 4 ) ^{2}} d x

\int x^{2} \cdot 4 - x^{2} d x

\int \frac{1}{x ( 2 + x )} d x

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

\int \frac{1}{x 2 x ^{2} - 3} d x

What is the integral of (300)/((3x+25)^2) ?
The integral of (300)/((3x+25)^2) is -(100)/(3x+25)+C