What is the integral of-y^{-1} ?

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

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integral of-y^{-1}

\int - y^{- 1} d y

- ln ∣ y ∣ + C

Solution steps

\int - y^{- 1} d y

Take the constant out:

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

= - \int y^{- 1} d y

Use the common integral:

\int y^{- 1} d y = ln (∣ y ∣)

= - ln ∣ y ∣

Add a constant to the solution

= - ln ∣ y ∣ + C