sin²(x).cos³(x).dx
= sin²(x).cos²(x).cos(x).dx
= sin²(x).(1-sin²(x)).cos(x).dx

Poser sin(x) = t
cos(x) dx = dt

sin²(x).cos³(x).dx = t²(1-t²)dt
sin²(x).cos³(x).dx = (t²-t^4)dt

Une primitive est donc:
(t³/3) - (t^5 /5)

soit (1/3).sin³(x) - (1/5).sin^5(x)
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Sauf distraction.