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#16 2011 MIT Integration Bee Qualifying Exam

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2 ways: integral ∫(x-a)/(x+a) dx
2:21

2 ways: integral ∫(x-a)/(x+a) dx

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2nd way: integral ∫ log √x(x^n) dx
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2nd way: integral ∫ log √x(x^n) dx

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

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2nd/3ways: trig integral ∫sec(x) dx
1:46

2nd/3ways: trig integral ∫sec(x) dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)
4:59

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

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2 ways: sq root derivative 1/(√√(1/√x))
7:33

2 ways: sq root derivative 1/(√√(1/√x))

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Calculus: Find nth derivative of log(ax+b)
3:51

Calculus: Find nth derivative of log(ax+b)

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3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2
3:49

3rd/3ways: sum Show 1+2+3+...+n = n(1+n)/2

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AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx
2:36

AP Calculus 2nd way: integral ∫(ax+c)/(ax^2 + bx) dx

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1st/2ways: permutation Show P(n,2)+P(n,1)=n^2
4:37

1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

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alternate way: count sum 1+2+3+ ... +n
4:02

alternate way: count sum 1+2+3+ ... +n

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3 Views

trig integral ∫cot(x) log(sin(x)) dx
1:57

trig integral ∫cot(x) log(sin(x)) dx

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matrix product: AB=0 where A≠0 & B≠0
1:35

matrix product: AB=0 where A≠0 & B≠0

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derivative log f(g(x)) (a)
1:47

derivative log f(g(x)) (a)

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Review: trig tan(x+360)= tan(x) & tan(x+180)=tan(x)
2:08

Review: trig tan(x+360)= tan(x) & tan(x+180)=tan(x)

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Lamar U: trig integral ∫cos^5(2t) sin^2(2t) dt
1:58

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

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2
3:16

Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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Princeton U: trig integral ∫sin(x)/√(1+cos(x)) dx
1:43

Princeton U: trig integral ∫sin(x)/√(1+cos(x)) dx

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integral ∫x^(n-1)/(1+x^n) dx
1:15

integral ∫x^(n-1)/(1+x^n) dx

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Evaluate the integrals
1:42

Evaluate the integrals

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