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1.11 H: Integration

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Question 175

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

1.11 H: Integration Questions

  1. A Level
  2. /Maths
  3. /1.11 H: Integration

480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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