What is the integral of 2y^{-1} ?

The integral of 2y^{-1} is 2ln|y|+C

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integral of 2y^{-1}

\int 2 y^{- 1} d y

2 ln ∣ y ∣ + C

Solution steps

\int 2 y^{- 1} d y

Take the constant out:

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

= 2 \cdot \int y^{- 1} d y

Use the common integral:

\int y^{- 1} d y = ln (∣ y ∣)

= 2 ln ∣ y ∣

Add a constant to the solution

= 2 ln ∣ y ∣ + C