The value of -cos5xcos xdx iswhere C is constant of integration

Let nbsp; I=∫cos5xcos xdx =∫(cos5x+cos3x) (cos3x+cos x)+cos xcos xdx =∫2(cos4x cos2x)cos x+ cos xcos xdx =∫(2(cos 4x cos2x)+1)dx =sin4x2 sin2x+x+C ...

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Standard XII

Physics

Examples

The value of ...

Question

The value of $\int \frac{cos 5 x}{cos x} d x$ is
(where $C$ is constant of integration)

\frac{sin 4 x}{2} - \frac{sin 2 x}{2} + \frac{x}{2} + C

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\frac{sin 4 x}{2} - sin 2 x + x + C

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\frac{sin 4 x}{2} - cos 2 x + x + C

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\frac{cos 4 x}{2} - cos 2 x + 2 x + C

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Solution

The correct option is B $\frac{sin 4 x}{2} - sin 2 x + x + C$
Let
$I = \int \frac{cos 5 x}{cos x} d x = \int \frac{(cos 5 x + cos 3 x) - (cos 3 x + cos x) + cos x}{cos x} d x = \int \frac{2 (cos 4 x - cos 2 x) cos x + cos x}{cos x} d x = \int (2 (cos 4 x - cos 2 x) + 1) d x = \frac{sin 4 x}{2} - sin 2 x + x + C$

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The value of ∫cos5xcosxdx is (where C is constant of integration)

The correct option is B sin4x2−sin2x+x+CLet I=∫cos5xcosxdx =∫(cos5x+cos3x)−(cos3x+cosx)+cosxcosxdx =∫2(cos4x−cos2x)cosx+cosxcosxdx =∫(2(cos4x−cos2x)+1)dx =sin4x2−sin2x+x+C

The value of $\int \frac{cos 5 x}{cos x} d x$ is
(where $C$ is constant of integration)