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

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

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integral of-3x^{-1}

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

- 3 ln ∣ x ∣ + C

Solution steps

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

Take the constant out:

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

= - 3 \cdot \int x^{- 1} d x

Use the common integral:

\int x^{- 1} d x = ln (∣ x ∣)

= - 3 ln ∣ x ∣

Add a constant to the solution

= - 3 ln ∣ x ∣ + C