What is the integral of ((x-3))/(x+3) ?

The integral of ((x-3))/(x+3) is -6ln|x+3|+x+C

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integral of ((x-3))/(x+3)

\int \frac{( x - 3 )}{x + 3} d x

- 6 ln ∣ x + 3 ∣ + x + C

Solution steps

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

\frac{x - 3}{x + 3} = - \frac{6}{x + 3} + 1

= \int - \frac{6}{x + 3} + 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{6}{x + 3} d x + \int 1 d x

\int \frac{6}{x + 3} d x = 6 ln ∣ x + 3 ∣

\int 1 d x = x

= - 6 ln ∣ x + 3 ∣ + x

Add a constant to the solution

= - 6 ln ∣ x + 3 ∣ + x + C

x^{2} - 11, - 2

\frac{d}{d x} (\frac{x}{4})

\int x^{- \frac{4}{3}} d x

\frac{d}{d x} ((x^{3} + 8) e^{x})

\frac{d}{d x} (3^{x} - 3 e^{π} + x^{3})

What is the integral of ((x-3))/(x+3) ?
The integral of ((x-3))/(x+3) is -6ln|x+3|+x+C