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

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

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integral of 1/(2z)

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

\frac{1}{2} ln ∣ z ∣ + C

Solution steps

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

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}{z} d z

Use the common integral:

\int \frac{1}{z} d z = ln (∣ z ∣)

= \frac{1}{2} ln ∣ z ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ z ∣ + C

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