What is the integral of (3x)/((x^2+5)^2) ?

The integral of (3x)/((x^2+5)^2) is -3/(2(x^2+5))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x)/((x^2+5)^2)

\int \frac{3 x}{( x ^{2} + 5 ) ^{2}} d x

- \frac{3}{2 ( x ^{2} + 5 )} + C

Solution steps

\int \frac{3 x}{( x ^{2} + 5 ) ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x}{( x ^{2} + 5 ) ^{2}} d x

Apply u-substitution

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

= 3 \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

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

Apply the Power Rule

: - \frac{1}{u}

= 3 \cdot \frac{1}{2} (- \frac{1}{u})

Substitute back

u = x^{2} + 5

= 3 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 5})

Simplify

3 \cdot \frac{1}{2} (- \frac{1}{x ^{2} + 5}) : - \frac{3}{2 ( x ^{2} + 5 )}

= - \frac{3}{2 ( x ^{2} + 5 )}

Add a constant to the solution

= - \frac{3}{2 ( x ^{2} + 5 )} + C

\frac{d}{d x} (\frac{11 - 11 x}{7 x ^{\frac{3}{7}}})

\frac{\partial}{\partial v} (\frac{1}{v})

\frac{d}{d x} (3 x^{2} - 12 x + 5)

y \cdot d x + x^{2} \cdot d y = 0

\int \frac{2}{x} d x

What is the integral of (3x)/((x^2+5)^2) ?
The integral of (3x)/((x^2+5)^2) is -3/(2(x^2+5))+C