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

The integral of (x-2)/(x+1) is -3ln|x+1|+x+C

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

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

- 3 ln ∣ x + 1 ∣ + x + C

Solution steps

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

\frac{x - 2}{x + 1} = - \frac{3}{x + 1} + 1

= \int - \frac{3}{x + 1} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{3}{x + 1} d x + \int 1 d x

\int \frac{3}{x + 1} d x = 3 ln ∣ x + 1 ∣

\int 1 d x = x

= - 3 ln ∣ x + 1 ∣ + x

Add a constant to the solution

= - 3 ln ∣ x + 1 ∣ + x + C

h \to 0 lim (\frac{f ( h ) ( 8 + h ) - f ( 8 )}{h})

(- 5, - 10), (- 1, 5)

\frac{( 2 - 5 s )}{s ^{2} + 9}

\frac{d}{d x} (\frac{1}{g ( x )})

\int 8^{3 x - 1} d x

What is the integral of (x-2)/(x+1) ?
The integral of (x-2)/(x+1) is -3ln|x+1|+x+C