What is the integral of-1/r ?

The integral of-1/r is -ln|r|+C

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integral of-1/r

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

- ln ∣ r ∣ + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{r} d r = ln (∣ r ∣)

= - ln ∣ r ∣

Add a constant to the solution

= - ln ∣ r ∣ + C

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