1st/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

Show Σa=na where k=1 to n

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

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

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

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

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Screen Recording 2024-05-10 at 5.41.07 PM

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Lamar U Calculus: #14 integral ∫ [9sin^5(3x)-2cos^3(3x)] csc^4(3x) dx

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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logic: Simplify the Boolean function F=XYZ+XY'Z+XYZ'

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UC Davis #3 2nd way: ∫(2-x)/(x^2+5x)dx [integration by partial fraction]

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Screen Recording 2024-02-22 at 10.09.39 PM

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1st/2 ways: MIT Integration Bee

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logic: Simplify the Boolean function F=AB+(AC)'+AB'C(AB+C)

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#6 2019 MIT Integration Bee Final

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Find dy/dx where x^y+y^x=1

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