What is the integral of 1/(2r) ?

The integral of 1/(2r) is 1/2 ln|r|+C

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integral of 1/(2r)

\int \frac{1}{2 r} d r

\frac{1}{2} ln ∣ r ∣ + C

Solution steps

\int \frac{1}{2 r} d r

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{r} d r

Use the common integral:

\int \frac{1}{r} d r = ln (∣ r ∣)

= \frac{1}{2} ln ∣ r ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ r ∣ + C

(- 5, - 2), (2, 4)

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