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🔥 Day 132 — 2025 MIT Integration Bee (Qualifying) Q16 Evaluate: ∫ [ sin(4x) * cos(x) ] / [ cos(2x) * sin(x) ] dx It looks nasty, but this one collapses fast. Expand sin(4x), cancel what you can, and the integrand turns into a simple power of cos. From there it’s a one-liner with the double-angle identity. 👉 Hints • sin(4x) = 2 sin(2x) cos(2x) = 4 sin x cos x cos(2x) • Most things cancel → 4 cos^2 x • Use cos^2 x = (1 cos 2x)/2 Would you spot the cancellations under time pressure? ⏱️ 💭 Comment
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