What is the integral of (2x+11)/((x+4)^2) ?

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

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integral of (2x+11)/((x+4)^2)

\int \frac{2 x + 11}{( x + 4 ) ^{2}} d x

- \frac{2 x + 11}{x + 4} + 2 ln ∣ x + 4 ∣ + C

Solution steps

\int \frac{2 x + 11}{( x + 4 ) ^{2}} d x

Apply Integration By Parts

: - \frac{2 x + 11}{x + 4} - \int - \frac{2}{x + 4} d x

= - \frac{2 x + 11}{x + 4} - \int - \frac{2}{x + 4} d x

\int - \frac{2}{x + 4} d x = - 2 ln ∣ x + 4 ∣

= - \frac{2 x + 11}{x + 4} - (- 2 ln ∣ x + 4 ∣)

Simplify

= - \frac{2 x + 11}{x + 4} + 2 ln ∣ x + 4 ∣

Add a constant to the solution

= - \frac{2 x + 11}{x + 4} + 2 ln ∣ x + 4 ∣ + C

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