commutative: ab=ba via "picture"

2 ways: log exp derivative ln(x) e^(2ln(x))

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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2nd way: integral ∫ log √x(x^n) dx

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

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2nd way: trig Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫ cos^2(x) sin^3(x) dx

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trig Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫ √(cos(x)-cos^3(x)) dx

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When a die was thrown the scores was an odd #. What is the prob. that it was a prime #?

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

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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Screen Recording 2024-05-11 at 8.55.54 PM

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Lamar U: #9 1st way: trig integral ∫sec^2(9x) tan^3(9x) dx

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prob stat: 2 ways Joe's mean mark for the physics tests for the term was 72.

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4 ways: derivative x(log(x)-1)

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UC Davis #14: trig integral ∫(sin(x)-cos(x))(sin(x)+cos(x))^5 dx

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prob stat a) Calculate the mean & the std deviation of 4 numbers 2,3,6,9

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#Screen Recording 2024-05-13 at 10.52.38 PM

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Find the 2nd-order partial derivatives of f(x,y)=2xy^2-3x^2+xy^3

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U Penn: Show that the following decomposition CANNOT hold ...

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JHU: integral ∫t^3 e^(t^2) dt

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