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Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?
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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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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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Pantun Melayu [Buah cempedak di luar pagar]
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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
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2nd way: integral ∫ log √x(x^n) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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AI 2008 Hindustan 2nd/2 ways: Evaluate trig integral ∫2cos(x)/(3 sin^3(x)) dx
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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx
#3 2010 MIT Integration Bee Qualifying Exam
exp integral ∫(1+e^x)/(1-e^x) dx
#16 2014 MIT Integration Bee Qualifying Exam
#19 2011 MIT Integration Bee Qualifying Exam
1st/2 ways: nPn, nP(n-1), nP(n-2)
Lamar U: #11 trig integral ∫csc^6(x/4) cot^4(x/4) dx
Lamar U: #13 trig integral ∫(2+7sin^3(x))/cos^2(x) dx