What is the integral of (-3)/x-9/(x^2) ?

The integral of (-3)/x-9/(x^2) is -3ln|x|+9/x+C

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integral of (-3)/x-9/(x^2)

\int \frac{- 3}{x} - \frac{9}{x ^{2}} d x

- 3 ln ∣ x ∣ + \frac{9}{x} + C

Solution steps

\int \frac{- 3}{x} - \frac{9}{x ^{2}} 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} d x - \int \frac{9}{x ^{2}} d x

\int \frac{- 3}{x} d x = - 3 ln ∣ x ∣

\int \frac{9}{x ^{2}} d x = - \frac{9}{x}

= - 3 ln ∣ x ∣ - (- \frac{9}{x})

Simplify

= - 3 ln ∣ x ∣ + \frac{9}{x}

Add a constant to the solution

= - 3 ln ∣ x ∣ + \frac{9}{x} + C

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What is the integral of (-3)/x-9/(x^2) ?
The integral of (-3)/x-9/(x^2) is -3ln|x|+9/x+C