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Question

Integrate:

Sin2x/Sin5xSin3x dx

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Solution

sin2x / (sin5x.sin3x)

= sin(5x-3x) / (sin5x.sin3x)

= (sin 5x cos 3x - cos 5x sin 3x)/ sin 5x sin 3x

= cot 3x - cot 5x

integral of cot x = ln | sin x|

so integral of cot nx = ln | sin nx|/n

so integral = ln | sin 3x|/3 - ln |sin 5x|/5 + C

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