What is the integral of (-1/y) ?

The integral of (-1/y) is -ln|y|+C

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integral of (-1/y)

\int (- \frac{1}{y}) d y

- ln ∣ y ∣ + C

Solution steps

\int - \frac{1}{y} d y

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{y} d y = ln (∣ y ∣)

= - ln ∣ y ∣

Add a constant to the solution

= - ln ∣ y ∣ + C