AP Calculus 4th way: exp ∫1/(1+e^x) dx via 3rd u-sub

derivative x^n vs n^x vs x^x

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

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

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logic Idempotent law show x=xVx

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

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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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Review: Linear form, Quadratic form & Bilinear form

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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

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

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STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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

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

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

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#17 2022 MIT Integration Bee Qualifying Exam

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

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#1 2019 MIT Integration Bee Final

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