Columbia U: 6th/6 ways Evaluate the indefinite integral ∫1/(1+e^x) dx

1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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

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Pantun Melayu [Buah cempedak di luar pagar]

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Pantun Melayu [Sorong papan tarik papan]

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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JHU: integral ∫t^3 e^(t^2) dt

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U Penn: Evaluate trig integral ∫(sin^2(x) -cos^2(x))/(sin(x)-cos(x))^2 dx

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#9 2023 MIT Integration Bee Qualifying Exam

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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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prob stat: An ordinary die is thrown. Find the prob. that the number obtained is

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Review: Multiplying each obs. by a CONSTANT results in new variance =

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prob stat: To obtain Grade A, Ben must achieve an average of at least 70 in 5 tests.

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prob stat: A candidate obtained the following results in her math examination:

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#23 2019 MIT Integration Bee Final

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#17 2010 MIT Integration Bee Qualifying Exam

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2nd way: trig sq rt Calculate integral ∫cos √x dx

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