1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2

CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd/3ways: trig integral ∫sec(x) dx

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2nd way: derivative (x^x)^x

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Loota Paagalpan Swastika Hindi Item Song Hindi Song

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2010 #2 MIT Integration Bee

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Median [special weighted mean]

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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logic [k map]: Simplify Boolean function F=X'Y'+X'Y+XY'+XY'

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prob stat: The discrete r.v. W has prob dist. as shown

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Lamar U 2nd way: evaluate integral ∫√(1+2ln(7x))/2 +10x^3/(x^4 +9) dx

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2nd way: Evaluate integral ∫x^2/√(19-x^2) dx

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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pascal triangle: count comb Show nCk = (n-1)Ck + (n-1)C(k-1)

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The sum of 3 numbers in AP is 15 & the sum of their squares is 3. Find the numbers.

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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2nd/2ways: [k map] logic Simplify the Boolean function F=AB+BC+B'C

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