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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2
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Pantun Melayu [Pulau Pandan Jauh Ke Tengah]
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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1st way: exp ∫(e^x)/x (1+x log(x)) dx
2nd/2 parts: sum Find the sum 2,3,14,24,37,... nth term
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2nd/2ways: count perm Show P(n,n)=P(n,n-1)
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2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))
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Alternate way: trig integral ∫sin(x) dx
3 ways: trig integral ∫tan(x) sec^2(x) dx
UT Austin: trig integral ∫cos(√x)/((√x) sin^2(√x)) dx
Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2
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Lamar U: trig integral ∫sin(13z) sin(4z) dz
Median [special weighted mean]
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Lamar U 2nd way: evaluate exp integral ∫e^(2x)/(1+e^(2x)) dx
Why the mean of AP is the median of AP? mean=median?
UC Davis #16: Prove (fgh)'=f'gh+fg'h+fgh' [differentiation using the product rule]
Princeton U: trig integral ∫sin(x)/√(1+cos(x)) dx
4 ways: trig integral ∫sin(x) cos(x) dx
3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))