What is the integral of (9x+25)/(x^2+10x+9) ?

The integral of (9x+25)/(x^2+10x+9) is 2ln|x+1|+7ln|x+9|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (9x+25)/(x^2+10x+9)

\int \frac{9 x + 25}{x ^{2} + 10 x + 9} d x

2 ln ∣ x + 1 ∣ + 7 ln ∣ x + 9 ∣ + C

Solution steps

\int \frac{9 x + 25}{x ^{2} + 10 x + 9} d x

Take the partial fraction of

\frac{9 x + 25}{x ^{2} + 10 x + 9} : \frac{2}{x + 1} + \frac{7}{x + 9}

= \int \frac{2}{x + 1} + \frac{7}{x + 9} d x

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{2}{x + 1} d x + \int \frac{7}{x + 9} d x

\int \frac{2}{x + 1} d x = 2 ln ∣ x + 1 ∣

\int \frac{7}{x + 9} d x = 7 ln ∣ x + 9 ∣

= 2 ln ∣ x + 1 ∣ + 7 ln ∣ x + 9 ∣

Add a constant to the solution

= 2 ln ∣ x + 1 ∣ + 7 ln ∣ x + 9 ∣ + C

\int 4 tan (x) sec^{7} (x) d x

\int \frac{1}{8 - x ^{2}} d x

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

\int \frac{4 x ^{3} + x + 1}{( x + 1 ) ( x ^{2} - x + 1 )} d x

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

What is the integral of (9x+25)/(x^2+10x+9) ?
The integral of (9x+25)/(x^2+10x+9) is 2ln|x+1|+7ln|x+9|+C