Mathematics

Mathematics

Problem

Compute ∫sin⁡2x cos⁡3x dx\displaystyle\int \sin^2 x\,\cos 3x\,dx. a) sin⁡3x6−sin⁡5x20+sin⁡x4+C\dfrac{\sin 3x}{6}-\dfrac{\sin 5x}{20}+\dfrac{\sin x}{4}+C b) sin⁡3x6−sin⁡5x20−sin⁡x4+C\dfrac{\sin 3x}{6}-\dfrac{\sin 5x}{20}-\dfrac{\sin x}{4}+C c) sin⁡3x6+sin⁡5x20+sin⁡x4+C\dfrac{\sin 3x}{6}+\dfrac{\sin 5x}{20}+\dfrac{\sin x}{4}+C d) sin⁡3x3−sin⁡5x10−sin⁡x2+C\dfrac{\sin 3x}{3}-\dfrac{\sin 5x}{10}-\dfrac{\sin x}{2}+C

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