2 ways: sq root √x^x

Careful: arc sin(sin(5π/4)) ≠ ...

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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logic Idempotent law show x=xVx

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Pantun Melayu [Buah cempedak di luar pagar]

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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examples 2x2 matrix withOUT an inverse

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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#10 2023 MIT Integration Bee Qualifying Exam

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

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Screen Recording 2024-02-22 at 10.30.06 PM

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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5 ways: trig derivative tan(x).

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Solve x(x-1)dy/dx - (x-2)y=x^3(2x-1) via Integrating Facto[IF]

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Do you know ... paper folding ...

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