trig Show cos(x)/(sec(x)+tan(x))=1-sin(x)

#10 2023 MIT Integration Bee Qualifying Exam

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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

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1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number

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derivative a^(f(x)g(x))^h(x)

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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okay lng ending nito

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Eps_8 Mei-Tabe

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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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Show that ar sinh(x) = ln(x + √ (x^2+1))

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Columbia U: 6th/6 ways Evaluate the indefinite integral ∫1/(1+e^x) dx

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2nd way: integral ∫x^2/(x^3 -2)^5 dx

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EP3 Aishiteru Game (Sub Indonesia)

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Alternate way: log integral ∫1/(bx+xln(ax)) dx

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EP4

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2nd way trig integral ∫(1-tan(x))/(1+tan(x)) dx

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