Q122. Integration.

Question 122.
Evaluate ∫ sin4x dx /(sin2x * sin3x).

Answer 122.
∫ sin 4x / (sin 2x * sin 3x) dx
= ∫ 2sin 2x cos 2x / (sin 2x * sin 3x) dx
= 2 ∫ (cos 2x / sin 3x) dx
= ∫ [ (2sin x * cos 2x) / (sin x * sin 3x) ] dx
= ∫ [ (sin 3x - sin x) / (sin x * sin 3x) ] dx
= ∫ cosec x dx - ∫ cosec 3x dx
= ln l tan(x/2) l - (1/3) ln l tan (3x/2) l + c.

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