Evaluate
\ln(|z|)+С
Differentiate w.r.t. z
\frac{1}{z}
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\ln(|z|)
Use \int \frac{1}{z}\mathrm{d}z=\ln(|z|) from the table of common integrals to obtain the result.
\ln(|z|)+С
If F\left(z\right) is an antiderivative of f\left(z\right), then the set of all antiderivatives of f\left(z\right) is given by F\left(z\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.
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