Find $$\(\int\left(12 \cos ^{3} x-4 \cos ^{3} 3 x\right) \mathrm{d} x\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w21_qp_23 Year：2021 Question No：7(c)
Answer:
Express integrand in form \(k_{1}(\cos 3 x+3 \cos x)+k_{2}(\cos 9 x+3 \cos 3 x)\)
Obtain correct integrand \(9 \cos x-\cos 9 x\)
Integrate to obtain form \(k_{3} \sin x+k_{4} \sin 9 x\)
Obtain correct \(9 \sin x-\frac{1}{9} \sin 9 x\)
Obtain correct integrand \(9 \cos x-\cos 9 x\)
Integrate to obtain form \(k_{3} \sin x+k_{4} \sin 9 x\)
Obtain correct \(9 \sin x-\frac{1}{9} \sin 9 x\)
Knowledge points:
2.5.2 use trigonometrical relationships in carrying out integration
Solution:
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