Using the substitution $u=\cos x$, find \(\displaystyle\displaystyle \displaystyle\int{\frac{\sin

Question

Using the substitution $u=\cos x$, find $\displaystyle\displaystyle \displaystyle\int{\frac{\sin 2x}{{{\cos }^{2}}x+\cos x+2}}\ \mathrm{d}x$, giving your answer in terms of $x$.[5]

Accepted Answer

$-\ln(\cos^2x+\cos x+2)+\dfrac2{\sqrt7}\tan^{-1}\!\left(\dfrac{2\cos x+1}{\sqrt7}\right)+C$

2023 ACJC P2 Q1

2023 ACJC P2 Q1

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