What is the integral of (x+3)/(x^2+5x+6) ?

The integral of (x+3)/(x^2+5x+6) is ln|x+2|+C

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integral of (x+3)/(x^2+5x+6)

\int \frac{x + 3}{x ^{2} + 5 x + 6} d x

ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{x + 3}{x ^{2} + 5 x + 6} d x

Apply u-substitution

: \int \frac{1}{u - 1} d u

= \int \frac{1}{u - 1} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

= ln ∣ x + 3 - 1 ∣

Simplify

= ln ∣ x + 2 ∣

Add a constant to the solution

= ln ∣ x + 2 ∣ + C

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What is the integral of (x+3)/(x^2+5x+6) ?
The integral of (x+3)/(x^2+5x+6) is ln|x+2|+C