U Penn: Show that the following decomposition CANNOT hold ...

2 way: exp integral e^(ax+b)/1+e^(ax+b)) dx

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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx

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Pantun Melayu [Buah cempedak di luar pagar]

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Columbia U: 9th/9 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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integration bee 2018 Swinburne U integral x^2/2 ln(2/x^2) dx

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Screen Recording 2024-05-12 at 8.34.35 PM

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Columbia U: 10th/10 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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Screen Recording 2024-05-12 at 9.04.39 PM

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Screen Recording 2024-05-13 at 9.18.43 PM

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logic: De Morgan's Law

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Columbia U: 8th/9 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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Screen Recording 2024-05-12 at 8.48.55 PM

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Screen Recording 2024-05-18 at 11.10.22 PM

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Screen Recording 2024-05-12 at 10.30.40 PM

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3 ways: sum Show 1+3+5+...nth term = n^2

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Screen Recording 2024-05-12 at 10.29.10 PM

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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Always ZERO

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Bachelor Point 2025 S05 (Ep01-08) Bengali

Doridro

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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2

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