2 ways: derivative ln(ax-b)^(p-qx)

#3 2024 MIT Integration Bee Qualifying Exam

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exp Differentiate (i) b^e^x (ii) b^x&e (iii) (b^e)^x (iv) (b^x)^e

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trig Write each expression as an equivalent algebraic expression involving only x.

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

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3rd/3ways: trig integral ∫sec(x) dx

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2010 Raytheon MATHCOUNTS National Competition

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prob stat: A normal 6-sided dice is rolled. What is the prob. that the first '6' occurs:

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2nd/3ways: sum Show 1+2+3+...+n=n(1+n)/2

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2nd/2 parts: 2 (elementary) rules

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2nd way: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫sin(x)cos(x)cos(4x)cos(8x)cos(16x)cos(32x)cos(64x) dx

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Review: Product to Sum Identities

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STPM Math T Sem.2 Exponential fun: Find the derivative (19)-(40)

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COMMON MISTAKE!: directive d/dx(sin(x) cos(x)) ≠ d/dx(sin(x)) d/dx(cos(x))

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

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1st/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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