derivative: If x=cos(log(y)), show that (1-x^2)y2 - xy1 = y

integration bee 2014 UNSW 3rd way: e^x(cos(x)+sin(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(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 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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

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

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2nd way: integral ∫ log √x(x^n) dx

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Screen Recording 2024-05-11 at 8.55.54 PM

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#Screen Recording 2024-05-13 at 10.52.38 PM

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2nd way: trig integral ∫√(sec^5(x)/sin^3(x)) dx

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Screen Recording 2024-05-11 at 9.02.49 PM

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Screen Recording 2024-05-12 at 9.04.39 PM

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U Arizona: For each integral decide which of the following is needed:

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Screen Recording 2024-05-13 at 9.18.43 PM

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1)integral ∫ x dx 2)integral ∫ ln(x)/x dx via inspection [NO u-sub]

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prob stat: X & Y are 2 events s.t P(x|y)=0.4, P(y)=0.25 & P(x)=0.2.

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Screen Recording 2024-05-12 at 10.30.40 PM

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2010 Raytheon MATHCOUNTS National Competition

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