solve-the-integrayion-sin2x-sin5xsin3x-

Question Number 28705 by students last updated on 29/Jan/18

s o l v e t h e i n t e g r a y i o n \frac{s i n 2 x}{s i n 5 x s i n 3 x}

Answered by mrW2 last updated on 30/Jan/18

\sin 2 x = \sin (5 x - 3 x) = \sin 5 x \cos 3 x - \cos 5 x \sin 3 x

\int \frac{\sin 2 x}{\sin 5 x \sin 3 x} d x = \int \cot 3 x d x - \int \cot 5 x d x

= \frac{\ln (\sin 3 x)}{3} - \frac{\ln (\sin 5 x)}{5} + C

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