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Techniques of Integration - Integration Using Partial Fractions

Techniques of Integration - Integration Using Partial Fractions

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

Solution:

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Answer:(i) \(\frac1{x-1}-\frac{x}{x^2+4}\). (ii) \(\ln|x-1|-\frac12\ln(x^2+4)+C\), \(x\ne1\).

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