3rd/3 ways: trig integral ∫ sin(ax+b) dx

exp integral e^x (f(x) + f'(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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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(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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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd way: integral ∫ log √x(x^n) dx

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UC Davis #14: integral ∫x √(4-x) dx

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prob stat: 2 formula for sample variance

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2nd/2parts example Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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COMMON MISTAKE: derivative (x)' 1/2 x^(-1/2)

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Find 1) E(X) 2) E(3X) 3) E(3x+2)

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#10 2023 MIT Integration Bee Qualifying Exam

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Evaluate these 9 integrals containing ...

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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Show ∫1/(a+btan(x)) dx = ...

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Screen Recording 2023-12-06 at 3.07.30 AM

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Alternate way: ∫(5+2x)/(x+x^4)dx

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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Screen Recording 2023-12-06 at 3.06.15 AM

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