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2nd/2ways: r-Permutations
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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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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1st/3 ways: Show 1+2+3+...+n=n(1+n)/2 via picture
derivative: If x=cos(log(y)), show that (1-x^2)y2 - xy1 = y
trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula
prob stat: 2 formula for sample variance
2nd/2ways: count perm Show P(n,n)=P(n,n-1)
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2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2
2nd way: integral ∫1/(a + √√b (x^2)) dx
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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0
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Consider the mode, median, mean.
trig integral ∫1/(cos^2(a+bx) √(p^2-qtan(a+bx)) )dx
sq root 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(√x (1+√x))dx
2nd way: log sq rt ∫ln(ax+b)/n√(ax+b)^m dx
3rd way: rational function integral ∫x^3/√ (1+x^2) dx
2nd/2ways: Taylor series of sin(x) [Maclaurin's series]
integration bee 2018 Swinburne integral (1-cos(x))/sin^2(x/2) dx