sinx + cos xsin x cos x

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Solution

The given function is sin 3 x+ cos 3 x sin 2 x cos 2 x .

sin 3 x+ cos 3 x sin 2 x cos 2 x = sin 3 x sin 2 x cos 2 x + cos 3 x sin 2 x cos 2 x = sinx cos 2 x + cosx sin 2 x =tanxsecx+cotxcosecx (1)

From (1), we get,

∫ sin 3 x+ cos 3 x sin 2 x cos 2 x dx = ∫ ( tanxsecx )dx + ∫ ( cotxcosecx ) dx =secx−cosecx+c

Thus, the integral of the function sin 3 x+ cos 3 x sin 2 x cos 2 x is secx−cosecx+c.

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