1st/3parts: Mean of 1,2,3,...,n SAME as Mean 1,n

Always ZERO

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Pantun Melayu [Buah cempedak di luar pagar]

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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2nd way: derivative (x^x)^x

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Pantun Melayu [Sorong papan tarik papan]

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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Pascal's triangle nth triangular number [examples]

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#ชีวิตชิวๆในต่างโลกกับอดีตผู้กล้า_#ขาดคุณนางฟ้าไปผมคงมีชีวิตต่อไปไม่ได้แล้ว

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UC Davis #14: integral ∫x √(4-x) dx

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alternate way: count sum 1+2+3+ ... +n

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Careful: arc sin(sin(5π/4)) ≠ ...

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2nd/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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alternate way: count sum 1+3+5+ ... +(2n-1)

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Evaluate these 8 integrals of the form ∫(a-bx)^m dx

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2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))

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

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logic: tautology p→q≡(¬q→¬p)

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UC Davis: 4 ways exp integral ∫7^(2x+3) dx

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5th/10parts: Material implication

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