What is the integral of (x-2)/(x+7) ?

The integral of (x-2)/(x+7) is -9ln|x+7|+x+C

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integral of (x-2)/(x+7)

\int \frac{x - 2}{x + 7} d x

- 9 ln ∣ x + 7 ∣ + x + C

Solution steps

\int \frac{x - 2}{x + 7} d x

\frac{x - 2}{x + 7} = - \frac{9}{x + 7} + 1

= \int - \frac{9}{x + 7} + 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{9}{x + 7} d x + \int 1 d x

\int \frac{9}{x + 7} d x = 9 ln ∣ x + 7 ∣

\int 1 d x = x

= - 9 ln ∣ x + 7 ∣ + x

Add a constant to the solution

= - 9 ln ∣ x + 7 ∣ + x + C

\int_{0}^{9} x^{2} - 6 x + 5 d x

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

y = 8 e^{8 e^{x} + x}

\int \frac{( cos ( x ) )}{x} d x

\frac{d ^{3}}{d x ^{3}} (sin (x^{3}))

What is the integral of (x-2)/(x+7) ?
The integral of (x-2)/(x+7) is -9ln|x+7|+x+C