Given that $y = \frac{3\ln 2x}{x^2}$ for $x 0$. Show that \(\frac{\mathrm{d}

Question

Given that $y = \frac{3\ln 2x}{x^2}$ for $x > 0$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{3}{x^3}(1 - 2\ln 2x)$.[3] Hence, find $\int \frac{\ln 2x}{x^3} \mathrm{d}x$.[3]

Accepted Answer

(a) $\frac{3}{x^3}(1 - 2\ln{2x}) $ (b) $ -\frac{1}{2} \left( \frac{\ln{2x}}{x^2} + \frac{1}{2x^2} \right) + C$

2024 FMSS PRELIMS P2 Q3

2024 FMSS PRELIMS P2 Q3