trig integral ∫1/(a^2+b tan(x)) dx

Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt

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Pantun Melayu [Sorong papan tarik papan]

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(203) Muling Nabuhay ang Pinakamalakas na Emperor sa katawan ng Isang Bata

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Careful: arc sin(sin(5π/4)) ≠ ...

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

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Difference of 2 nonconsecutive triangular numbers

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Show log b^n(x^m) = m/n logb(x)

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4th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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5th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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3 ways: Derivative y=x^(m/n)

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integral ∫x^2/√(x^2+a^2) dx

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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2nd way: If y=(ax-b)/(a-bx), prove that 2y1y3=3(y2)^2

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)

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1st/2ways: Taylor series of cos(x)

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Do you know ... in tagalog?

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exp integral ∫(e^x +1)^3 dx

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UT Austin: trig integral ∫(1-cos^2(x/2))^2 sin(x/2) dx

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2nd way: ∫e^x/(e^2x + 2e^x +5) dx

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1st/2 parts: Inverse 2x2 matrix

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