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$\int_{- \frac{π}{2}}^{\frac{π}{2}} \frac{\cos 6 x + 6 \cos 4 x + 15 \cos 2 x + 10}{\cos 5 x + 5 \cos 3 x + 10 \cos x} d x =$

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$π$

$2 π$

answer is D.

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Detailed Solution

$\cos 6 x + 6 \cos 4 x + 15 \cos 2 x + 10$

$= \cos 6 x + \cos 4 x + 5 (\cos 4 x + \cos 2 x) + 10 (\cos 2 x + 1)$

$= 2 \cos x (\cos 5 x + 5 \cos 3 x + 10 \cos x)$

$∴ I = \int_{- \frac{π}{2}}^{\frac{π}{2}} 2 \cos x d x = 4 \int_{0}^{\frac{π}{2}} \cos x d x = 4$

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