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Question
Find the integrals of the function:
sin3 x cos3 x
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Solution
Let `I = int sin^3 x cos^3 x dx`
`= int sin x . sin^2 x * cos^3 x dx`
`= int sin x (1 - cos^2 x)cos^3 x dx`
`= int (cos^3 x - cos^5 x) sin x dx`
Put cos x = t
⇒ - sin x dx = dt
`therefore I = int (t^3 - t^5)` dt
`= (- t)^4/4 + t^6/6 + C`
`= 1/6 cos^6 x - 1/4 cos^4 x + C`
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