Find $\displaystyle \displaystyle\int{\frac{x+2}{{{x}^{2}}+2x-3}},\mathrm{d}x$.[2] Find \(\display

Question

Find $\displaystyle \displaystyle\int{\frac{x+2}{{{x}^{2}}+2x-3}},\mathrm{d}x$.[2] Find $\displaystyle \displaystyle\int{2}x\sin x,\mathrm{d}x$.[2] Using the substitution $x=3\sin \theta $, find the exact value of $\displaystyle \displaystyle\int_{0}^{\frac{3}{2}}{\sqrt{9-{{x}^{2}}}}\,\mathrm{d}x$.[5]

Accepted Answer

(a) $\frac{1}{4}\ln|x+3| + \frac{3}{4}\ln|x-1| + C$, (b) $-2x\cos x + 2\sin x + C$, (c) $\frac{9\sqrt{3}}{8} + \frac{3\pi}{4}$

2024 ASRJC Promo Q9

2024 ASRJC Promo Q9

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