What is the integral of (-6)/(3x) ?

The integral of (-6)/(3x) is -2ln|x|+C

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integral of (-6)/(3x)

\int \frac{- 6}{3 x} d x

- 2 ln ∣ x ∣ + C

Solution steps

\int \frac{- 6}{3 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Simplify

= (- 2) \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= (- 2) ln ∣ x ∣

Simplify

= - 2 ln ∣ x ∣

Add a constant to the solution

= - 2 ln ∣ x ∣ + C

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