Screen Recording 2024-05-19 at 9.53.16 PM

sum Find 1/1.4 + 1/4.7 +1/7.10+... +1/((3n-2)(3n+1))

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1st way: exp ∫(e^x)/x (1+x log(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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trig Write each expression as an equivalent algebraic expression involving only x.

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

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2nd/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2

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

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trig integral ∫tan^n(x) dx where n is EVEN via Reduction formula

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2nd/2 ways: derivative x^2/3 + y^2/3 = a^2/3

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UC Davis #11: count prove Σi^2 = n(n+1)(2n+1)/6 where i=1 to n

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Always ZERO

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Show integral ∫x √(ax+b) dx = 2(3ax-2b)√(ax+b)^3 /(15a^2)

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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2nd way: ∫e^x/(e^2x + 2e^x +5) dx

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2nd way: integral ∫log n√(ax+b)(ax+b) dxx

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

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trig log integral ∫sin(ln(x^n)) dx

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#11 2019 MIT Integration Bee Final

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🍯🙏🥺7

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