Additional Mathematics 0606 / Logarithmic and exponential functions / 3.133.13: Partial fractions integral with ln0606/12/M/J/22 — Question 7 · 8 marks · Log laws, EquationsMark as done · Save for later · Show all solutions(a)Show that 22x+3−1x−1+1(x−1)2\dfrac{2}{2x + 3} - \dfrac{1}{x - 1} + \dfrac{1}{(x - 1)^{2}}2x+32−x−11+(x−1)21 can be written as 8−3x(x−1)2(2x+3)\dfrac{8 - 3x}{(x - 1)^{2}(2x + 3)}(x−1)2(2x+3)8−3x.[2]▸ Answer(b)Find ∫2a8−3x(x−1)2(2x+3) dx\displaystyle\int_{2}^{a}\frac{8 - 3x}{(x - 1)^{2}(2x + 3)}\,\mathrm{d}x∫2a(x−1)2(2x+3)8−3xdx where a>2a > 2a>2. Give your answer in the form c+lndc + \ln dc+lnd, where ccc and ddd are functions of aaa.[6]▸ Answer▸ Official mark scheme← 3.37: Log equation with base 33.14: Normal to y = ln(x² + 2x + 1) form curve →
