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

= - \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))

\frac{\partial}{\partial x} (3 x^{4} - 65 x^{3})

\int_{0}^{\frac{π}{6}} cos (3 x) d x

y^{^{''}} + y = cos (t), y (0) = 0, y^{^{'}} (0) = 0

x \to - 3 + lim (ln (x + 3))

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