What is the integral of (3x)^{-1} ?

The integral of (3x)^{-1} is 1/3+1/3 ln|x|+C

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integral of (3x)^{-1}

\int (3 x)^{- 1} d x

\frac{1}{3} + \frac{1}{3} ln ∣ x ∣ + C

Solution steps

\int (3 x)^{- 1} d x

Apply Integration By Parts

: \frac{1}{3} - \int - \frac{1}{3 x} d x

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

\int - \frac{1}{3 x} d x = - \frac{1}{3} ln ∣ x ∣

= \frac{1}{3} - (- \frac{1}{3} ln ∣ x ∣)

Simplify

= \frac{1}{3} + \frac{1}{3} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{3} + \frac{1}{3} ln ∣ x ∣ + C

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What is the integral of (3x)^{-1} ?
The integral of (3x)^{-1} is 1/3+1/3 ln|x|+C