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evaluate the following integral ∫ sin 2x / sin 5x sin 3x dx

evaluate the following integral
∫ sin 2x / sin 5x sin 3x dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello student,
Please find the answer to your question below

I = \int \frac{sin2x}{sin5xsin3x}dx
I = \int \frac{sin(5x-3x)}{sin5xsin3x}dx
I = \int \frac{sin5xcos3x-cos5xsin3x}{sin5xsin3x}dx
I = \int \frac{cos3x}{sin3x}dx - \int \frac{cos5x}{sin5x}dx
I = log(cosec3x) - \int \frac{cos5x}{sin5x}dx
I = log(cosec3x) - log(cosec5x) + c

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