2 ways: exp log integral ∫3^(log81(x)) dx

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]

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

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

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

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Pantun Melayu [Sorong papan tarik papan]

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Pantun Melayu [Sorong papan tarik papan]

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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

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

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logic Idempotent law show x=xVx

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logic Idempotent law show x=xVx

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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#17 2012 MIT Integration Bee Qualifying Exam

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#17 2012 MIT Integration Bee Qualifying Exam

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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prob stat: One sample of n=4 scores has a mean of M=10, &

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prob stat: One sample of n=4 scores has a mean of M=10, &

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Texas Tech: 5 ways trig Differentiate g(x)=cos^2(x)

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Texas Tech: 5 ways trig Differentiate g(x)=cos^2(x)

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

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

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#2 2011 MIT Integration Bee Qualifying Exam

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#2 2011 MIT Integration Bee Qualifying Exam

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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#12 2012 MIT Integration Bee Qualifying Exam

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#12 2012 MIT Integration Bee Qualifying Exam

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1st part: Mean 1+2+3+...+n is just (1+n)/2. Why?

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1st part: Mean 1+2+3+...+n is just (1+n)/2. Why?

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1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2

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1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2

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2nd way: derivative x^n w.r.t x^x

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2nd way: derivative x^n w.r.t x^x

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