0606 P22 - Jun 2017 - Q5 - 5 marks
8597
(i) Show that
\(\frac{d}{dx}\left[0.4x^5\left(0.2-\ln(5x)\right)\right]=kx^4\ln(5x),\)
where \(k\) is an integer to be found.
(ii) Express \(\ln(125x^3)\) in terms of \(\ln(5x)\).
(iii) Hence find \(\int x^4\ln(125x^3)\,dx\).
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