What is the integral of (6x+3)/(x^2+11x+28) ?

The integral of (6x+3)/(x^2+11x+28) is -7ln|x+4|+13ln|x+7|+C

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integral of (6x+3)/(x^2+11x+28)

\int \frac{6 x + 3}{x ^{2} + 11 x + 28} d x

- 7 ln ∣ x + 4 ∣ + 13 ln ∣ x + 7 ∣ + C

Solution steps

\int \frac{6 x + 3}{x ^{2} + 11 x + 28} d x

Take the partial fraction of

\frac{6 x + 3}{x ^{2} + 11 x + 28} : - \frac{7}{x + 4} + \frac{13}{x + 7}

= \int - \frac{7}{x + 4} + \frac{13}{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{7}{x + 4} d x + \int \frac{13}{x + 7} d x

\int \frac{7}{x + 4} d x = 7 ln ∣ x + 4 ∣

\int \frac{13}{x + 7} d x = 13 ln ∣ x + 7 ∣

= - 7 ln ∣ x + 4 ∣ + 13 ln ∣ x + 7 ∣

Add a constant to the solution

= - 7 ln ∣ x + 4 ∣ + 13 ln ∣ x + 7 ∣ + C

n = 2 \sum \infty \frac{1}{4 ^{2 n}}

\int \frac{1}{4 x ^{2} + 12 x + 18} d x

\frac{\partial}{\partial x} (4 + x^{3} + y^{3} - 3 x y)

2 e^{- t} - \frac{3}{2} e^{- 2 t}

\frac{d}{d x} (sec (x) - 2 cos (x))

What is the integral of (6x+3)/(x^2+11x+28) ?
The integral of (6x+3)/(x^2+11x+28) is -7ln|x+4|+13ln|x+7|+C