Techniques of Integration - Integration Using Partial Fractions

Techniques of Integration - Integration Using Partial Fractions

IP 4

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

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Answer:(i) \(\dfrac1x-\dfrac{x}{x^2+1}\) (ii) \(\ln|x|-\dfrac12\ln(x^2+1)+C,\ x\neq0\)

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