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UC Davis #12 [THE INTEGRATION OF RATIONAL FUNCTIONS] withOUT u-sub

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

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Review: Linear form, Quadratic form & Bilinear form

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integral ∫ x dx withOUT using Power rule.
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integral ∫ x dx withOUT using Power rule.

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exp integral ∫10^x e^(10x) dx

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Discrete rv X has the following prob. distribution
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Discrete rv X has the following prob. distribution

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

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

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#13 2011 MIT Integration Bee Qualifying Exam
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#13 2011 MIT Integration Bee Qualifying Exam

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2nd way: integral ∫x^(n-1) /(a-bx^n) dx
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2nd way: integral ∫x^(n-1) /(a-bx^n) dx

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#2 2024 2nd/2 ways: MIT Integration Bee Qualifying Exam
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#2 2024 2nd/2 ways: MIT Integration Bee Qualifying Exam

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#18 2011 MIT Integration Bee Qualifying Exam
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#18 2011 MIT Integration Bee Qualifying Exam

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2nd way: exp integral ∫e^(a√x)/√x dx

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AP Calculus 2nd way: trig integral ∫1/(cos^2(x) √(1+tan(x)) dx
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AP Calculus 2nd way: trig integral ∫1/(cos^2(x) √(1+tan(x)) dx

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#2 2023 MIT Integration Bee Qualifying Exam
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#2 2023 MIT Integration Bee Qualifying Exam

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Columbia U: 9th/9 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub
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Columbia U: 9th/9 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

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#8 2022 MIT Integration Bee Qualifying Exam
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#8 2022 MIT Integration Bee Qualifying Exam

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2nd/2 ways: MIT Integration Bee
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2nd/2 ways: MIT Integration Bee

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

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Laman utama>UC Davis #12 [THE INTEGRATION OF RATIONAL FUNCTIONS] withOUT u-sub>