5 ways: integral ∫a^(px+q) dx

#10 2023 MIT Integration Bee Qualifying Exam

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

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

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

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

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Review: Linear form, Quadratic form & Bilinear form

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

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2nd way: trig integral ∫1/(1+sec(x)) dx

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

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prob stat: The following frequency table gives the values obtained

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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2nd way: ∫(x+3)/(x^2+6x)^2 dx vs ∫(x+3)(x^2+6x)^2 dx

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UC Davis #10: count prove Σi = n(n+1)/2 where i=1 to n

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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2nd way: integral ∫x/(2ax-x^2) dx

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3 ways: exp integral ∫ln(e^x) + ln(e^(-x)) dx

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#3 UC Davis integrate ∫3/(4+x^(1/3)) dx via power sub

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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) dx

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Sum of the first n integers 1+2+3+ ...+n=n/2 (1+n) via Induction

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doneScreen Recording 2024-05-18 at 10.25.20 PM

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