Given that
5x+3(x−1)(3x+1)2≡Ax−1+B3x+1+C(3x+1)2\frac{5x+3}{(x-1)(3x+1)^2} \equiv \frac{A}{x-1} + \frac{B}{3x+1} + \frac{C}{(3x+1)^2}(x−1)(3x+1)25x+3≡x−1A+3x+1B+(3x+1)2C
find the values of the constants AAA, BBB and CCC.
Hence find the exact value of
∫235x+3(x−1)(3x+1)2 dx\int_{2}^{3} \frac{5x+3}{(x-1)(3x+1)^2} \,\mathrm{d}x∫23(x−1)(3x+1)25x+3dx
giving your answer in the form plnq+rp \ln q + rplnq+r where ppp, qqq and rrr are rational numbers.
Practise Edexcel A Level Maths 11.7 Partial Fractions with exam-style questions for A Level Maths. 19 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.