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

The integral of (x+2)/(x-2) is x-2+4ln|x-2|+C

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

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

x - 2 + 4 ln ∣ x - 2 ∣ + C

Solution steps

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

Expand

\frac{x + 2}{x - 2} : \frac{x}{x - 2} + \frac{2}{x - 2}

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

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

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

= x - 2 + 2 ln ∣ x - 2 ∣ + 2 ln ∣ x - 2 ∣

Simplify

= x - 2 + 4 ln ∣ x - 2 ∣

Add a constant to the solution

= x - 2 + 4 ln ∣ x - 2 ∣ + C

f (x) = \frac{1}{x + 8}, at x = 5

x \to 4 - lim (\frac{( 1 - x )}{4 - x})

cos (6 x) (\frac{d y}{d x}) + 6 (tan (6 x)) y = 5 sec (6 x)

t \to 0 lim (cos (\frac{1}{t}))

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

What is the integral of (x+2)/(x-2) ?
The integral of (x+2)/(x-2) is x-2+4ln|x-2|+C