What is the integral of (x+2)/((x+1)^2) ?

The integral of (x+2)/((x+1)^2) is -(x+2)/(x+1)+ln|x+1|+C

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integral of (x+2)/((x+1)^2)

\int \frac{x + 2}{( x + 1 ) ^{2}} d x

- \frac{x + 2}{x + 1} + ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{x + 2}{( x + 1 ) ^{2}} d x

Apply Integration By Parts

: - \frac{x + 2}{x + 1} - \int - \frac{1}{x + 1} d x

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

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

= - \frac{x + 2}{x + 1} - (- ln ∣ x + 1 ∣)

Simplify

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

Add a constant to the solution

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

\int_{0}^{10} 9800 π (10 - y) d y

f (x) = \frac{- x ^{2}}{200}

\frac{d}{d x} ((x^{2} + 1) (x + 5 + \frac{1}{x}))

y = 4 x^{2}, y = 24

f (x) = 2 x^{3} - 2 x, at x = 1

What is the integral of (x+2)/((x+1)^2) ?
The integral of (x+2)/((x+1)^2) is -(x+2)/(x+1)+ln|x+1|+C