What is the integral of 1/(x^2+11x+28) ?

The integral of 1/(x^2+11x+28) is 1/3 ln|x+4|-1/3 ln|x+7|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x^2+11x+28)

\int \frac{1}{x ^{2} + 11 x + 28} d x

\frac{1}{3} ln ∣ x + 4 ∣ - \frac{1}{3} ln ∣ x + 7 ∣ + C

Solution steps

\int \frac{1}{x ^{2} + 11 x + 28} d x

Take the partial fraction of

\frac{1}{x ^{2} + 11 x + 28} : \frac{1}{3 ( x + 4 )} - \frac{1}{3 ( x + 7 )}

= \int \frac{1}{3 ( x + 4 )} - \frac{1}{3 ( x + 7 )} 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{1}{3 ( x + 4 )} d x - \int \frac{1}{3 ( x + 7 )} d x

\int \frac{1}{3 ( x + 4 )} d x = \frac{1}{3} ln ∣ x + 4 ∣

\int \frac{1}{3 ( x + 7 )} d x = \frac{1}{3} ln ∣ x + 7 ∣

= \frac{1}{3} ln ∣ x + 4 ∣ - \frac{1}{3} ln ∣ x + 7 ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ x + 4 ∣ - \frac{1}{3} ln ∣ x + 7 ∣ + C

y^{^{'}} = 5 x^{4} e^{- x^{5}} + e^{x}

n = 0 \sum \infty n! 2^{n} n^{- n}

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 8

y = \frac{x ^{x}}{sin ( x )}

x \to 2 lim (\frac{x ^{3} + 8}{x - 2})

What is the integral of 1/(x^2+11x+28) ?
The integral of 1/(x^2+11x+28) is 1/3 ln|x+4|-1/3 ln|x+7|+C