AP Calculus 4th way: exp ∫1/(1+e^x) dx via 3rd u-sub

Let f(x) be a polynomial of degree 1. If f(10)-f(5)=15, then f(20)-f(5)=?

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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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 way: integral ∫ log √x(x^n) dx

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

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Pantun Melayu [Buah cempedak di luar pagar]

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2 ways of "counting" (a+b)^2 = a^2+2ab+b^2

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2 ways: trig integral ∫sec^2(ax+b) tan(ax+b) dx

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2 ways: trig integral cos^2(x) sin^2(x) dx

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2 ways: integral 1 dx

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Show that the function u(x,y)=e^x cos(y) is harmonic in the x-y plane

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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 2024-02-22 at 10.06.31 PM

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2 ways of "counting": 1=1/2+1/4+1/8+1/16+ ...

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2 ways of "counting": Angles in a triangles = 180 degrees

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