Additional Mathematics 0606 / Calculus — Integration / 2.722.72: Logarithmic curve and integration0606/23/O/N/17 — Question 9 · 9 marksMark as done · Save for later · Show all solutions(i)Show that ddx(lnxx3)=1−3lnxx4\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac{\ln x}{x^{3}}\right) = \dfrac{1 - 3\ln x}{x^{4}}dxd(x3lnx)=x41−3lnx.[3]▸ Answer(ii)Find the exact coordinates of the stationary point of the curve y=lnxx3y = \dfrac{\ln x}{x^{3}}y=x3lnx.[3]▸ Answer(iii)Use the result from part (i) to find ∫lnxx4 dx\displaystyle\int \frac{\ln x}{x^{4}}\,\mathrm{d}x∫x4lnxdx.[4]▸ Answer▸ Official mark scheme← 2.51: Tangent to a quadratic and shaded area1.33: Integrating an exponential and finding a second derivative →
