Columbia U: 10th/10 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

derivative If y=acos(log(x)) + bsin(log(x)), prove that x^2y2+xy1+y=0

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

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2nd way: integral ∫ log √x(x^n) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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derivative Find d2y/dx2 for this function y=ln(x)/(1-x)

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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0

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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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2nd way: log sqr integral ∫ln(x)/x dx

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1st/2 ways: MIT Integration Bee

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2nd way: trig integral ∫ 1/( √3 sin(x) + cos(x)) dx

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Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx

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#15 2022 MIT Integration Bee Qualifying Exam

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2nd way:exp sq rt integral ∫1/( √x e^(a√x -b)) dx

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1st/2 way: MIT Integration Bee Final ∫ x^4/(1-x^2) dx

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2nd way: sq rt integral ∫ √√e^x dx

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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2nd way: integral ∫ 1/(1+x+x^2) dx

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