What is the integral of (x+1)/((x+3)^2) ?

The integral of (x+1)/((x+3)^2) is ln|x+3|+2/(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 (x+1)/((x+3)^2)

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

ln ∣ x + 3 ∣ + \frac{2}{x + 3} + C

Solution steps

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

Expand

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{x}{( x + 3 ) ^{2}} d x = ln ∣ x + 3 ∣ + \frac{3}{x + 3}

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

= ln ∣ x + 3 ∣ + \frac{3}{x + 3} - \frac{1}{x + 3}

Simplify

ln ∣ x + 3 ∣ + \frac{3}{x + 3} - \frac{1}{x + 3} : ln ∣ x + 3 ∣ + \frac{2}{x + 3}

= ln ∣ x + 3 ∣ + \frac{2}{x + 3}

Add a constant to the solution

= ln ∣ x + 3 ∣ + \frac{2}{x + 3} + C

\int 0.8 e^{x} d x

\int \frac{7}{( 2 x ) ^{5}} d x

\int x (x^{2} + 1)^{7} d x

\int \frac{2 x}{5 x ^{2} 16 x ^{2} - 9} d x

\int - 36

What is the integral of (x+1)/((x+3)^2) ?
The integral of (x+1)/((x+3)^2) is ln|x+3|+2/(x+3)+C