Integration with partial fractions

Express a rational function in partial fractions, then integrate to find area or evaluate a definite integral.

1 questions · Standard +0.3

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WJEC Unit 3 2023 June Q8
7 marks Standard +0.3
The function \(f\) is defined by \(f(x) = \frac{4x^2 + 12x + 9}{2x^2 + x - 3}\), where \(x > 1\).
  1. Show that \(f(x)\) can be written as \(2 + \frac{5}{x-1}\). [3]
  2. Hence find the exact value of \(\int_3^7 f(x)\,dx\). [4]