Additional Mathematics 0606 / Equations, inequalities and graphs / 3.43.4: Combine fractions and integrate0606/12/F/M/22 — Question 4 · 6 marksMark as done · Save for later · Show all solutions(a)Show that 12x−1+4(2x−1)2\dfrac{1}{2x - 1} + \dfrac{4}{(2x - 1)^{2}}2x−11+(2x−1)24 can be written as 2x+3(2x−1)2\dfrac{2x + 3}{(2x - 1)^{2}}(2x−1)22x+3.[1]▸ Answer(b)Find ∫252x+3(2x−1)2 dx\displaystyle\int_{2}^{5} \dfrac{2x + 3}{(2x - 1)^{2}}\,\mathrm{d}x∫25(2x−1)22x+3dx, giving your answer in the form a+ln ba + \mathrm{ln}\,ba+lnb, where aaa and bbb are constants.[5]▸ Answer▸ Official mark scheme← 3.35: Inequality and distinct real roots3.6: Intersection of an ellipse and y=3/(2x)y = 3/(2x)y=3/(2x) →
