UC Davis #8: exp integral ∫e^x (1-e^x)(1+e^x)^10 dx

When the sister found out that her brother had a girlfriend...

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

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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Pantun Melayu [Buah cempedak di luar pagar]

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

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

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2nd way: integral ∫ log √x(x^n) dx

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Screen Recording 2024-05-11 at 8.58.53 PM

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2nd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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Screen Recording 2024-05-12 at 8.48.55 PM

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prob stat: x̄=∑xk where k=1,2,3,...,n?

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2nd Alt. way: log Taylor series of ln(sec(x)) withOUT Taylor series explicitly

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Screen Recording 2024-05-11 at 9.09.07 PM

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A function f is called even if f(-x)=f(x) for ALL x in the domain of f &

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3rd/3ways: Laplace Show that ...

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

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STPM Math T Sem2 Ex11.3 Find the first four terms in the Maclaurin series ...

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2 ways: trig integral ∫ sin(ax+b) dx

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count comb Show (n-r)* nCr = n * (n-1)Cr

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