trig Show (sec(x)+1)/sec^2(x) = sin^2(x)/(sec(x)-1)

2nd/2 parts: sum Find the sum 2,3,14,24,37,... nth term

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2nd/3ways: trig integral ∫sec(x) dx

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(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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Pantun Melayu [Sorong papan tarik papan]

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

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2nd/2ways: add math sum a + (a+d) + (a+2d) + ... + (a+(n-1)d) ?

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Conversion: Permutation - Combination vice versa

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Show Σ(a+bk) = (a+1/2bn)(n+1)

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2 ways: derivative a^f(g(x))

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sq root integral ∫1/√...√√x dx with n √

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derivative y=a^(arc sin(x))^2

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Review: trig sin(x)= cos(90-x) = cos(x-90) prefer

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exp integral ∫e^x/((a+e^x)(b+e^x)) dx

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Georgia Tech MA155: Evaluate each indefinite integral:

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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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Screen Recording 2024-05-13 at 9.18.43 PM

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2nd way: trig 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(a sin^2(x) + b cos^2(x)) dx

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Logical Equivalence

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