AP Calculus 3rd way: exp integral 1/(1+e^x) dx [withOUT u-sub]

prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.

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2nd way: integral ∫ log √x(x^n) 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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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 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Screen Recording 2024-05-10 at 5.37.05 PM

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Screen Recording 2024-05-06 at 11.51.42 PM

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NYU: 3 ways ∫(1+ln(x))/x dx

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prob stat The members of an orchestra were asked how many instruments each could play.

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exp Evaluate these 4 integrals containing e^x ...

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Screen Recording 2024-05-05 at 11.29.37 PM

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Screen Recording 2024-05-06 at 11.55.08 PM

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Screen Recording 2024-05-13 at 10.55.21 PM

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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Lamar U 2nd way: evaluate integral ∫√(1+2ln(7x))/2 +10x^3/(x^4 +9) dx

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prob stat: 1st/2 parts. One sample has a mean of M=6 &

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2nd way: exp integral ∫(e^(-x) - e^x)/(e^(2x) + e^(-2x) 2) dx

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Screen Recording 2024-05-11 at 9.09.07 PM

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