The one where trigonometry dominates \(x\)!

Calculus Level 5

\[ \large \displaystyle I = \int_{0}^{\pi/2} \frac{\cos (x) \sin (2x) \sin(3x)}{x} \, dx \]

\(I\) is given as above. Find the value of \( \lfloor 1000I \rfloor \).


Notation: \(\lfloor \cdot \rfloor\) denotes the floor function or greatest integer function.

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