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

UC Davis #6 integral e^x(1+2e^x)^4 dx

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

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(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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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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2nd way: trig integral ∫sin(x/a) dx

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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prob stat: Two events are such that P(A)=0.6, P(B)=0.5 & P(AUB)=0.85

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#17 2022 MIT Integration Bee Qualifying Exam

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trig integral sin(x+sin(x))-sin(x-sin(x)) dx

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

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prob stat: A normal 6-sided dice is rolled. What is the prob. that the first '6' occurs:

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2 ways: exp log integral ∫3^(log81(x)) dx

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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#1 2024 MIT Integration Bee Qualifying Exam

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trig integral ∫x/(1+x) dx vs ∫cos(x)/(1+cos(x)) dx

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2nd way: integral ∫1/x log mb(x) dx

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log sq rt integral ∫√x ln(x) dx withOUT u-sub

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