What is the integral of ((5x+7))/(x^2+4x+4) ?

The integral of ((5x+7))/(x^2+4x+4) is 5ln|x+2|+3/(x+2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((5x+7))/(x^2+4x+4)

\int \frac{( 5 x + 7 )}{x ^{2} + 4 x + 4} d x

5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + C

Solution steps

\int \frac{5 x + 7}{x ^{2} + 4 x + 4} d x

Expand

\frac{5 x + 7}{x ^{2} + 4 x + 4} : \frac{5 x}{x ^{2} + 4 x + 4} + \frac{7}{x ^{2} + 4 x + 4}

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{5 x}{x ^{2} + 4 x + 4} d x + \int \frac{7}{x ^{2} + 4 x + 4} d x

\int \frac{5 x}{x ^{2} + 4 x + 4} d x = 5 (ln ∣ x + 2 ∣ + \frac{2}{x + 2})

\int \frac{7}{x ^{2} + 4 x + 4} d x = - \frac{7}{x + 2}

= 5 (ln ∣ x + 2 ∣ + \frac{2}{x + 2}) - \frac{7}{x + 2}

Simplify

5 (ln ∣ x + 2 ∣ + \frac{2}{x + 2}) - \frac{7}{x + 2} : 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2}

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2}

Add a constant to the solution

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + C

\frac{d}{d x} (10000 - 9000 e^{- 0.3 x})

\frac{d}{d x} (\frac{x ^{2}}{e ^{3 - 4 x}})

\frac{9}{sin ( x ) + cos ( x )}

\frac{d}{d x} (\frac{3 x}{8})

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

What is the integral of ((5x+7))/(x^2+4x+4) ?
The integral of ((5x+7))/(x^2+4x+4) is 5ln|x+2|+3/(x+2)+C