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Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Find $\int \log x d x$
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Answer

We take log x as the first function and the constant function 1 as the second function. 
Hence, $\int(\log x ).1 d x=\log x \int 1 d x-\int\left[\frac{d}{d x}(\log x) \int 1 d x\right] d x$ 
= $(\log x) \cdot x-\int \frac{1}{x} x d x=x \log x-x+C$

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