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what is the integral of log x w.r.t. x

$\int \log x ⅆ x = \log x \int ⅆ x - \int (\int ⅆ x . \frac{ⅆ}{ⅆ x} \log x) ⅆ x = \log x \int ⅆ x - \int (x . \frac{1}{x}) ⅆ x = \log x \int ⅆ x - \int ⅆ x = x \log x - x + C = x (\log x - 1) + C$

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