UT Austin: sq root ∫(1+√x)^3/√x dx

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

manhwa_Recap

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Alternate way: 2nd picture Show 1+3+5+...+(2n-1)=n^2

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

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There are 2 lines. One line has 3 points & the other line has 6 points.

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"baby" fact: exp even odd e^x

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

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2nd way: rational function integral ∫x^3/√ (1+x^2) dx

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

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4th way: rational function integral ∫x^3/√ (1+x^2) dx

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Screen Recording 2024-02-16 at 8.23.14 PM

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Solve the differential equation xcos^2(y) dx + tan(y) dy=0

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Review: Arithmetic Series a+(a+d)+(a+2d)+...+(a+(n-1)d)=

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Given events J & K:

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multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.

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2nd/2ways: derivative (sin(x)+cos(x))^2

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exp integral ∫e^x/((a+e^x)(b+e^x)) dx

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The pth, qth, & rth terms of an AP are x,y,z respectively.

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Alternate way: trig integral ∫cot(x) csc^6(x) dx ... just in 1 line.

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prob stat 2/2 ways: A couple has 6 children whose ages are 6,8,10,12,14,16.

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integral ∫x^3/(x+2) dx

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