Logical equivalent involving ... tautology & contradiction

STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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logic Idempotent law show x=xVx

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

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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

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Lamar U 2nd way: evaluate trig integral ∫17(xe^x+e^x)sin(e^x)-14sin(x) dx

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Jewel Jam Lobaton Da

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Alternate way: ∫(5+2x)/(x+x^4)dx

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Screen Recording 2024-02-16 at 8.27.04 PM

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AP Calculus 2nd way: trig integral ∫sin^2(x) cos^2(x) dx

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9Screen Recording 2023-12-02 at 2.43.56 AM

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

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#6 2024 MIT Integration Bee Qualifying Exam

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exp integral ∫10^x e^(10x) dx

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1st/2ways: Taylor series of sin(x)

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Columbia U: 1st way integral ∫√(x^2-9)/x^4 dx

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Roorkee 1976 RET 1991Hindustan: trig integral 1/(sin^2(x) cos^2(x)) dx

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Screen Recording 2024-02-22 at 10.18.05 PM

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8Screen Recording 2023-12-07 at 1.55.57 AM

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