Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

TGM Original Questions

Find \(\frac{\mathrm{d}}{\mathrm{d}x}(x^2\ln 3x)\). Hence, find \(\displaystyle\displaystyle \displaystyle\int x\ln 3x \, \mathrm{d}x.\)

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Answer:\(\displaystyle\int x\ln(3x)\,\mathrm dx=\frac12x^2\ln(3x)-\frac14x^2+C\)

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