MIT Integration Bee Qual. Exam #1: integral x^(1/log(x)) dx

Bijection of elements in tn & a pair of elements of (n+1)

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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Pantun Melayu [Sorong papan tarik papan]

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

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2nd way: derivative (x^x)^x

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Compute the derivatives of the following function

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Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c

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Quickie: 6169^2 - 2331^2?

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2 ways: Find a formula for d/dx[f^m(x) g^n(x)], where f & g are differentiable functions ...

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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2

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2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)

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exp integral e^x (f(x) + f'(x)) dx

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1st/2parts: Linear interpolation (2 given points)

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2nd/3part: Maclaurin Series [ahp kia]

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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1st/3 parts: Growing patterns

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U of Auckland: proc & stat Let X be a continuous random variable with p.d.f

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4 ways: Evaluate Σ(2k+1) k=1,20

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【Zhu Ling’er ASMR Eating Ears】The little ghost sticks their ear 👂 out

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exp integral ∫ (e^2x -1) /(e^2x +1)dx

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