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2nd way: trig integral ∫1/(sin(x) cos^2(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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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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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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4ways: exp trig integral ∫ e^(cos^2(x)) sin(2x) dx
Polite number
2 ways: sq root derivative 1/(√√(1/√x))
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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2
alternate way: count sum 1+2+3+ ... +n
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CMU integral ∫1/(x^2 √(16x^2 -19)) dx
integral ∫logb(√x) dx
1st/2ways: r-Permutations
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2 ways: trig integral ∫sin(√x) dx
Which pairs are equivalent via truth table?
2 ways: integral ∫x/(x+a) dx
1st/2ways: Find trig integral ∫sec^2(x)/csc^2(x) dx
trig integral cos(a√x +b) dx
Find the number of subsets {1,{2,3}}