1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture

CMU integral ∫1/(x^2 √(16x^2 -19)) dx

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logic Idempotent law show x=xVx

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2 ways: sq root derivative 1/(√√(1/√x))

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2nd way: integral ∫e^(x/2)/(1+e^x) dx

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3ways: Find a formula for the sum 2+4+6+...+2n

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A 2 digit number is equal to the sum of the product of its digits & the sum of its digits.

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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)

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Review: trig sin(x+90)= cos(x) & cos(x+90)=-sin(x)

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2nd way: trig integral 1/(cot(x)-tan(x)) dx

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Find the power set of each of the following sets ...

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3 ways: trig integral ∫tan(x) sec^2(x) dx

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UC Davis #8: integral cos(5x)/(3+sin(5x)) dx

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UT Austin: trig sq root integral ∫1/(sin(x) + cos(x)) dxsin(√x)/√(x cos^3(√x)) dx

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Screen Recording 2024-02-16 at 9.14.39 PM

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

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integral (a-x)/(b-x) dx

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2nd/2 ways: inverse trig derivative show d(arc sin(x))/dx = 1/√(1-x^2)

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#18 2010 MIT Integration Bee Qualifying Exam

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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2nd way: derivative y^2=4a(x+a sin(x/a))

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