Techniques of Integration - Integration Using Partial Fractions
Techniques of Integration - Integration Using Partial Fractions
Express \(\frac{5x-1}{x^2-1}\) in partial fractions. Hence, evaluate \(\displaystyle\displaystyle \displaystyle\int_{2}^{3} \frac{5x-1}{x^2-1} \, \mathrm{d}x\).
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Answer:\(\frac{5x-1}{x^2-1}=\frac2{x-1}+\frac3{x+1}\), and hence \(\int_2^3\frac{5x-1}{x^2-1}\,\mathrm dx=8\ln2-3\ln3\)
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