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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Similar questions

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

\int \frac{s i n 2 x}{s i n 5 x s i n 3 x} d x

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

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

\int \frac{sin 2 x}{sin 5 x sin 3 x} d x = \frac{1}{3} log | sin 3 x | - f (x)

f (x) =

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