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

Why the mean of AP is the median of AP? mean=median?

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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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Bijection of elements in tn & a pair of elements of (n+1)

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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logic Idempotent law show x=xVx

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lim x/e^x? as x→∞

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

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Pantun Melayu [Sorong papan tarik papan]

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Pantun Melayu [Buah cempedak di luar pagar]

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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A cubical die, numbered 1 to 6 is weighted so that a six is twice as likely to occur as any other #.

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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Conversion: Permutation - Combination vice versa

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4 ways: trig integral ∫tan(x) dx

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prob stat: The following frequency table gives the values obtained

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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