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Grade 12Integral Calculus

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

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 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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