2023TrialShort answer

Q13 (c) (ii)

2 marks

Question

Hence find

\int \frac{10}{(x+1)(x^2+4)}\,dx.

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Solution

\begin{aligned} \int\frac{10}{(x+1)(x^2+4)}\,dx &=\int\frac{2}{x+1}+\frac{-2x+2}{x^2+4}\,dx\\ &=\int\frac{2}{x+1}-\frac{2x}{x^2+4}+\frac{2}{x^2+4}\,dx\\ &=2\ln|x+1|-\ln|x^2+4|+\tan^{-1}\frac{x}{2}+C \end{aligned}

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Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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