Integrating the natural log by parts

Question

What is $\displaystyle\int\ln x\,dx$ ?

Short answer

$x\ln x-x+C$ . Treat the integrand as $1\cdot\ln x$ and integrate by parts: $x\ln x-\int x\cdot\frac{1}{x}dx$ . Differentiating the answer returns $\ln x$ .

Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 3.2 Integration, 'Basics of integration A', p.35; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Integration Strategy
The Fundamental Theorem of Calculus
Indefinite Integrals, the Net Change Theorem, and the Substitution Rule