#12 2014 MIT Integration Bee Qualifying Exam

Learning English is more fun!

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]

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Lamar U: Use log. differentiation to find the 1st derivative of the given function

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Calculus: If u=f(x+cy)+g(x-cy) then uxx / uyy ?

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#8 2021 MIT Integration Bee Qualifying Exam

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If y=a e^(mx) + b e^(-mx), show that y2=m^2y

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AP Calculus 2nd way trig ∫sin^3(x)/(cos(x)-1) dx

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20-may workshop

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AP Calculus 2nd way trig integral ∫x^2 cos(x) dx

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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#6 2010 MIT Integration Bee Qualifying Exam

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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0

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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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Columbia U: 1st way integral ∫√(x^2-9)/x^4 dx

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

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Median [special weighted mean]

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