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Integrate ln(x) dx

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Answer

\boxed{x \ln(x) - x + C}

Differentiating our result yields $\frac{d}{dx}(x \ln(x) - x + C) = (\ln(x) + 1) - 1 = \ln(x)$ , which confirms the integration is correct.

Problem: Evaluate the indefinite integral $\int \ln(x) \, dx$ .

Steps

Integration by parts (using $u = \ln(x)$ and $dv = dx$ ) $x \ln(x) - \int x \cdot \frac{1}{x} \, dx$
Simplify the integrand $x \ln(x) - \int 1 \, dx$
Integrate $x \ln(x) - x + C$

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