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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)

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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)

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

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

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2 ways: sq root derivative 1/(√√(1/√x))

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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)

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2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)

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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx

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2nd way: ∫2x/(x+5)^6 dx vs ∫2x (x+5)^6 dx

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Find the number of digits in mole [6.02x10^23]

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Find the number of digits in mole [6.02x10^23]

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Screen Recording 2024-02-16 at 8.27.04 PM

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2 ways: exp derivative a^(logb(cos(px+q))

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2 ways: exp derivative a^(logb(cos(px+q))

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2nd way: ∫1/(√(x-α)(x-β)) dx

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2nd way: ∫1/(√(x-α)(x-β)) dx

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#6 2024 MIT Integration Bee Qualifying Exam

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#6 2024 MIT Integration Bee Qualifying Exam

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prob stat: A die with 4 red faces & 2 green faces is rolled twice.

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prob stat: A die with 4 red faces & 2 green faces is rolled twice.

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5 ways: integral ∫a^(px+q) dx

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5 ways: integral ∫a^(px+q) dx

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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prob stat In a sample of n= 6 scores, 5 of the scores are each above the mean by one point.

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Screen Recording 2024-02-22 at 10.06.31 PM

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