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Differentiation of a Function

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Question

$\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x$

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Solution

$\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x = \int \frac{\sin (5 x - 3 x)}{\sin 5 x \sin 3 x} d x = \int \frac{\sin 5 x \cos 3 x - \cos 5 x \sin 3 x}{\sin 5 x \sin 3 x} d x = \int \frac{\sin 5 x \cos 3 x}{\sin 5 x \sin 3 x} - \frac{\cos 5 x \sin 3 x}{\sin 5 x \sin 3 x} d x = \int [\cot 3 x - \cot 5 x] d x = \int co t 3 x d x - \int \cot 5 x d x = \frac{1}{3} \ln |\sin 3 x| - \frac{1}{5} \ln |\sin 5 x| + C$

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\int \frac{sin 2 x}{sin 5 x sin 3 x} d x

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Differentiation of a Function

Standard XII Mathematics

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