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Techniques of Integration - Integration Using Partial Fractions

Techniques of Integration - Integration Using Partial Fractions

IP 4
  1. Express \(\frac{4x + 3}{(x - 4)(x^2 + 3)}\) as the sum of its partial fractions.
  2. Hence find \(\int \frac{4x + 3}{(x - 4)(x^2 + 3)} \mathrm{d}x\)

Solution:

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Answer:(i) \(\dfrac1{x-4}-\dfrac{x}{x^2+3}\) (ii) \(\ln|x-4|-\dfrac12\ln(x^2+3)+C\), on an interval with \(x\ne4\).

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