3 picture views of the sum ... 1+2+3+...+n

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

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2 ways: sq root √x^x

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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2 ways: sq root derivative 1/(√√(1/√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/3ways: trig integral ∫sec(x) dx

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2nd way: integral ∫ log √x(x^n) dx

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Swinburne U 2nd way: e^(-e^x) e^x dx

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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)

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Only those who've only studied Shuihu can truly understand each other, as expected.

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Screen Recording 2024-05-13 at 9.18.43 PM

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2nd way: Evaluate integral ∫x^2/√(19-x^2) dx

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Screen Recording 2024-05-12 at 8.48.55 PM

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2 ways: trig exp derivative e^(sin(x)) sin(e^x)

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exp trig derivative x^x sin(x)

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Screen Recording 2024-05-05 at 11.16.06 PM

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Screen Recording 2024-05-10 at 6.28.27 PM

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Screen Recording 2024-05-10 at 6.17.33 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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Screen Recording 2024-05-05 at 11.22.54 PM

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