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Question 597

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​
a.

find the values of the constants AAA, BBB and CCC.

[4]
b.

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+3​dx

giving your answer in the form pln⁡q+rp \ln q + rplnq+r where ppp, qqq and rrr are rational numbers.

[5]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

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