1st/2 ways[Direct]: Prove that the sum of 2 ODD numbers is ALWAYS EVEN

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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2nd way: integral ∫ log √x(x^n) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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

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3 ways: derivative a^(f(x)g(x))

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derivative a^(f(x)g(x))^h(x)

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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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

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Lamar U: Assume that x=x(t) & y=y(t) & differentiate the following equation wrt t

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

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#6 2019 MIT Integration Bee Final

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Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt

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Suppose E & F are 2 complementary events. Must E & F be mutually exclusive? Explain your answer.

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logic: Simplify the Boolean function F=AB+BC+B'C

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1st/3parts: Mean of 1,2,3,...,n SAME as Mean 1,n

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trig Show ...

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NYU: 2 ways integral ∫(x^2 + 2x +1) dx

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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