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

n = 1 \sum \infty \frac{n ^{7}}{7 ^{n}}

y^{^{'}} + 5 y = 8, y (0) = 0

\frac{d}{d x} (x 100 - x^{2})

\int \frac{1}{x ^{5}} - \frac{1}{x} d x

x^{^{''}} - 8 x^{^{'}} + 17 x = 0

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