alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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

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UC Davis #1: 2 ways Find the length of the graph for y=3x+2 on the closed interval ...

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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

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Review: Linear form, Quadratic form & Bilinear form

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logic Idempotent law show x=xVx

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exp integral ∫10^x e^(10x) dx

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matrix example: How to select the column you want ...

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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#12 UC Davis: Find the length of the graph for x=ln(y)=y^2/8 on the closed interval ...

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2nd way: exp integral e^3x/(e^x +2) dx withOUT u-sub

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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Purdue U: Evaluate ∫sec^5/2(x) tan(x) dx where x= 0 to pi/3

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8Screen Recording 2023-12-07 at 1.55.57 AM

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#3 2010 MIT Integration Bee Qualifying Exam

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2 ways: trig integral cos^2(x) sin^2(x) dx

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exp Calculate ∫x^3 3^x dx via IBP

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NYU: compute ∫ln(x)/x^2 dx

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#17 2011 MIT Integration Bee Qualifying Exam

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