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🔥 Day 152 — 2026 MIT Integration Bee (Qualifying) Q18 365 Problems for 365 Days Evaluate: Integral of (sin^2(x)/x^2 − sin(2x)/x) dx This one is a “recognize the derivative” speed problem. The integrand looks messy, but it’s literally the derivative of a super simple expression if you think “quotient rule trig identity.” If you try to integrate directly, it’s pain. If you spot the structure, it’s instant. Hints: \t•\tLook for something like (sin^2 x)/x \t•\tDifferentiate it with the quotient rul
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🔥 Day 139 — 2026 MIT Integration Bee (Qualifying) Q2 Evaluate: ∫ e^(2026·e^x) · e^x dx This is a perfect u-sub “inside-the-exponential” setup. If you set u = 2026·e^x, then du = 2026·e^x dx and the integral collapses immediately. 👉 Hints • u = 2026·e^x • du = 2026·e^x dx → (e^x dx) = du/2026 • Integral becomes (1/2026) ∫ e^u du Would you catch the substitution in time? ⏱️ 💭 Drop your answer below 👇 ✅ Full step-by-step solution is on my page. ➡️ Follow for the rest of the 2026 Qualifying set!
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