What is the integral of (2x+8)/((x+3)^2) ?

The integral of (2x+8)/((x+3)^2) is -(2x+8)/(x+3)+2ln|x+3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x+8)/((x+3)^2)

\int \frac{2 x + 8}{( x + 3 ) ^{2}} d x

- \frac{2 x + 8}{x + 3} + 2 ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{2 x + 8}{( x + 3 ) ^{2}} d x

Apply Integration By Parts

: - \frac{2 x + 8}{x + 3} - \int - \frac{2}{x + 3} d x

= - \frac{2 x + 8}{x + 3} - \int - \frac{2}{x + 3} d x

\int - \frac{2}{x + 3} d x = - 2 ln ∣ x + 3 ∣

= - \frac{2 x + 8}{x + 3} - (- 2 ln ∣ x + 3 ∣)

Simplify

= - \frac{2 x + 8}{x + 3} + 2 ln ∣ x + 3 ∣

Add a constant to the solution

= - \frac{2 x + 8}{x + 3} + 2 ln ∣ x + 3 ∣ + C

\int \frac{9}{x ^{2} + 16} d x

\int t^{24} e^{- t^{25}} d t

x \to 0 lim ((x)^{3 x})

\int \frac{x ^{3} + x + 1}{x ( x ^{2} + 1 )} d x

y = 9 x, y = x^{2} - 10

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