UC Davis #11 [THE INTEGRATION OF RATIONAL FUNCTIONS] withOUT u-sub

2nd way: integral ∫ log √x(x^n) dx

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exp integral ∫10^x e^(10x) dx

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

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

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

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2 ways: sq root derivative 1/(√√(1/√x))

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

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Roorkee 1976 RET 1991Hindustan: trig integral 1/(sin^2(x) cos^2(x)) dx

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#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt

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#13 2011 MIT Integration Bee Qualifying Exam

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#17 2022 MIT Integration Bee Qualifying Exam

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UC Davis: integrate sin(x)/(1+sin(x)) dx

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After a boy urinates, why doesn’t he use a tissue to wipe?

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#8 2014 MIT Integration Bee Qualifying Exam

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2nd way: integral ∫e^(x/2)/(1+e^x) dx

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Home grown organic vegetables

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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#2 2012 MIT Integration Bee Qualifying Exam

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