Hence, find \int \frac{2x^2 + 4}{(x^2 + 4)^2} \, dx. Use the substitution x = 2\tan\theta.
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Practise this question\int \sin x \cos 2x \, dx.[5 marks]\int_0^{\frac{\pi}{2}} \sin x \cos 2x \, dx.[2 marks]f(x) = x|x| = \begin{cases} x^2 &; x \ge 0 \\ -x^2 &; x < 0 \end{cases}. Use the trapezium rule with four intervals to calculate the area between f(x)…[5 marks]\frac{2x^2 + 4}{(x^2 + 4)^2} = \frac{2}{x^2 + 4} - \frac{4}{(x^2 + 4)^2}.[6 marks]More practice: the rest of this paper · more Integration II questions · all CAPE Pure Mathematics Unit 2 past papers