MIT Integration Bee Quali Exam 2023 #13 ∫(x+e+1)x^e e^x dx

stat: SLR Properties of residuals

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

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

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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2nd/3ways: trig integral ∫sec(x) dx

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

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Find the expected value & the variance of a geometric r.v. X

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2nd way: integral ∫ 1/(5x^2 -3x +7) dx with BONUS

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exp integral ∫10^x e^(10x) dx

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1st way: Calculate integral ∫x^2 (x+1)^9 dx

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sqrt integral ∫(√x+1)/(x+√x) dx

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Screen Recording 2024-02-21 at 10.02.50 PM

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Screen Recording 2024-05-12 at 8.48.55 PM

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2nd/2 ways: #1 2019 MIT Integration Bee Final

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#13 2011 MIT Integration Bee Qualifying Exam

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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#15 2022 MIT Integration Bee Qualifying Exam

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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2nd way: integral ∫x^2 (x+1)^9 dx via withOUT u-sub

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Find the number of permutations of the letters of the word ALLAHABAD

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