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

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

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

\int \frac{x + 6}{( x + 2 ) ^{2}} d x

- \frac{x + 6}{x + 2} + ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{x + 6}{( x + 2 ) ^{2}} d x

Apply Integration By Parts

= - \frac{x + 6}{x + 2} - \int - \frac{1}{x + 2} d x

\int - \frac{1}{x + 2} d x = - ln ∣ x + 2 ∣

= - \frac{x + 6}{x + 2} - (- ln ∣ x + 2 ∣)

Simplify

= - \frac{x + 6}{x + 2} + ln ∣ x + 2 ∣

Add a constant to the solution

= - \frac{x + 6}{x + 2} + ln ∣ x + 2 ∣ + C

\frac{d}{d x} (in sin (x))

\int_{0}^{\frac{π}{6}} cos (3 x) d x

x \to 0 lim (\frac{3 x ^{2} - 8 x}{x})

x \to \infty lim (x^{2} - 2)

\frac{d}{d x} (x^{l n (3 x)})

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