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#4 2024 MIT Integration Bee Qualifying Exam

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derivative (f(x)/g(x))^h(x)

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

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1st way: exp ∫(e^x)/x (1+x log(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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logic Idempotent law show x=xVx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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Review: Linear form, Quadratic form & Bilinear form

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prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.
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prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.

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prob stat: The following frequency table gives the values obtained
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prob stat: The following frequency table gives the values obtained

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

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

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UC Davis #6 integral e^x(1+2e^x)^4 dx
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UC Davis #6 integral e^x(1+2e^x)^4 dx

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#6 2010 MIT Integration Bee Qualifying Exam

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Home grown organic vegetables

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logic Show by truth table x∧(x→y)→y is Tautology
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logic Show by truth table x∧(x→y)→y is Tautology

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#8 2021 MIT Integration Bee Qualifying Exam
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#8 2021 MIT Integration Bee Qualifying Exam

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

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