Additional Mathematics 0606 / Logarithms and Exponents / 3.63.6: Definite integrals with fractional powers and ln0606/12/F/M/24 — Question 7 · 9 marks · Exponentials, Log lawsMark as done · Save for later · Show all solutions(a)Find ∫24(5x−2)−2/3 dx\displaystyle\int_{2}^{4}(5x - 2)^{-2/3}\,\mathrm{d}x∫24(5x−2)−2/3dx, giving your answer in exact form.[4]▸ Answer(b)Find ∫01/2(42x+1+8(2x+1)2)dx\displaystyle\int_{0}^{1/2}\left(\frac{4}{2x + 1} + \frac{8}{(2x + 1)^{2}}\right)\mathrm{d}x∫01/2(2x+14+(2x+1)28)dx, giving your answer in the form a+lnba + \ln ba+lnb, where aaa and bbb are integers.[5]▸ Answer▸ Official mark scheme← 3.5: Normal to y = ln(x³ + 3)3.7: Equation with log base 2 and reciprocal base →
