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CMU integral ∫1/(x^2 √(16x^2 -19)) dx
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2nd way: integral ∫ log √x(x^n) dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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Median [special weighted mean]
Mohammad Ali Jinnah University: Integrate the followings.
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2nd/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via "picture".
1st/3 parts: Growing patterns
1st/3parts: Mean of 1,2,3,...,n SAME as Mean 1,n
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2 ways: trig integral ∫ sin(ax+b) dx
3 ways: rational function integral ∫(x^2+1)/(x-1)^3 dx
CMU trig integral ∫sin^6(x) cos^3(x) dx
2nd/3 parts: Growing patterns
logic: tautology p→q≡(¬q→¬p)
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Florida International U: Find derivatives ...defined implicitly ... (a)-(c)
1st/2 ways: derivative y=(ln(x))^x
1st/2ways: logic Import-Export
2nd part: n^2 = (tn - tn-1)^2 where tn = nth triangular number