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Cloud Opening On a Small Scale
2:50
This integral looks impossible...until you see this #integration #calculuswithij #cbseclass12
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Мемы из ТикТока Иррациональное уравнение — это уравнение, содержащее неизвестное под знаком корня √ {\\displaystyle \\surd } или возведённое в степень, которую нельзя свести к целому числу. Простейшим примером иррационального уравнения является уравнение x = 2 {\\displaystyle {\\sqrt {x}}=2} или x 3 = − 3 {\\displaystyle {\\sqrt[{3}]{x}}=-3}. Иногда корни могут обозначать в виде рациональных степеней неизвестной, то есть вместо x n {\\displaystyle {\\sqrt[{n}]{x}}} пишут x 1 n {\\displaystyle x^
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🔥 Day 124 — 2025 MIT Integration Bee (Qualifying) Q7 Evaluate: ∫ [ x*log(x)cos(x) − sin(x) ] / [ xlog(x)^2 ] dx This looks nasty… until you reorganize it. Rewrite the integrand so the structure screams “reverse quotient rule.” If you can spot the right function in the numerator/denominator pairing, the antiderivative pops out immediately. 👉 Hints • Rearrange as: [ log(x)*cos(x) − (sin(x)/x) ] / [ log(x)^2 ]. • Ask: whose derivative has that exact pattern? Would you recognize it under speed-run
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🔥 Day 129 — 2025 MIT Integration Bee (Qualifying) Q13 Evaluate: ∫ [e^(2x)(x^2 x)] / ( (x^2 e^(2x))^2 1 ) dx Looks scary, but there’s a clean substitution hiding in plain sight. If you spot the right “u”, the whole thing turns into a tiny arctan. 👉 Hint: try u = x^2 e^(2x) Would you catch it under time pressure? ⏱️ 💭 Comment your approach below 👇 ✅ Full step-by-step solution is on my page. ➡️ Follow for the full MIT Qualifying set (20 days) 📈 #math #mathematics #calculus #integration #uSubst
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🔥 Day 91 — Can you solve this? Evaluate the integral: ∫ (x^2 1) / (x^3 1) dx It looks messy — but factoring saves the day 🧩 Split into simple pieces and each one integrates instantly. 👉 The trick? Factor x^3 1 = (x 1)(x^2 − x 1), do partial fractions, then finish with a log arctan combo 👀 Would you get the exact antiderivative before time runs out? ⏱️ 💭 Drop your answer below 👇 ✅ Full step-by-step solution is already on my page. ➡️ Follow for the rest of 100 Math Problems in 100 Days 📈 #m
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