3 ways: derivative log(x+ (1+√(x^2)))

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

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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

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logic Idempotent law show x=xVx

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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exp integral ∫a^x/b^x dx

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

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Find the number of different 8 letter arrangements that can be made from the letters of the word ..

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

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integral ∫x^2/√(x^2+a^2) dx

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2nd way: derivative x^n w.r.t x^x

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UC Davis #12: exp integrate ∫(27e^(9x) + e^(12x))^(1/3) dx

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prob stat: 2 formula for sample variance

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UC Davis #14: integral ∫x √(4-x) dx

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2nd way: trig integral ∫1/(cos(x)(1+cos(x)) dx

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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The pth, qth, & rth terms of an AP are x,y,z respectively.

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Bijection of elements in tn & a pair of elements of (n+1)

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"baby" fact: exp e^(ix)

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