What is the integral of 3/(x+2)-4/(x+5) ?

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

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integral of 3/(x+2)-4/(x+5)

\int \frac{3}{x + 2} - \frac{4}{x + 5} d x

3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{3}{x + 2} - \frac{4}{x + 5} 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{3}{x + 2} d x - \int \frac{4}{x + 5} d x

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

\int \frac{4}{x + 5} d x = 4 ln ∣ x + 5 ∣

= 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣

Add a constant to the solution

= 3 ln ∣ x + 2 ∣ - 4 ln ∣ x + 5 ∣ + C

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