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

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

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

\int (\frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{2}}) d x

5 ln ∣ x + 2 ∣ + \frac{3}{x + 2} + C

Solution steps

\int \frac{5}{x + 2} - \frac{3}{( x + 2 ) ^{2}} 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{5}{x + 2} d x - \int \frac{3}{( x + 2 ) ^{2}} d x

\int \frac{5}{x + 2} d x = 5 ln ∣ x + 2 ∣

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

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

Simplify

= 5 ln ∣ x + 2 ∣ + \frac{3}{x + 2}

Add a constant to the solution

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

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