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#14 MIT 2022 Integration Bee Qualifying Exam

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3rd way: nCr = (n-1)Cr + (n-1)C(r-1)
2:47

3rd way: nCr = (n-1)Cr + (n-1)C(r-1)

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Review: Linear form, Quadratic form & Bilinear form
9:02

Review: Linear form, Quadratic form & Bilinear form

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1st way: exp ∫(e^x)/x (1+x log(x)) dx
1:49

1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd way: integral ∫ log √x(x^n) dx
1:00

2nd way: integral ∫ log √x(x^n) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
0:50

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
1:11

CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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2 ways: exp integral ∫(p^x + q^x)/r^x dx
2:50

2 ways: exp integral ∫(p^x + q^x)/r^x dx

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2nd/3ways: exp Derivative x^x
0:56

2nd/3ways: exp Derivative x^x

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integral ∫(2x+3)/(4x^2+1) dx
1:25

integral ∫(2x+3)/(4x^2+1) dx

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exp integral ∫1/(e^(ax+b) (1+e^(ax+b)) dx
2:08

exp integral ∫1/(e^(ax+b) (1+e^(ax+b)) dx

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Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c
2:57

Alternate way: trig integral ∫sec(x) dx= ln(tan(/π4+x/2)) + c

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integral ∫(x^2+2x)/(x^2+2x+2) dx
1:22

integral ∫(x^2+2x)/(x^2+2x+2) dx

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2 ways: log derivative y=ln(a+b)
0:46

2 ways: log derivative y=ln(a+b)

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2nd/4ways: trig derivative sin(x)
0:51

2nd/4ways: trig derivative sin(x)

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trig integral ∫1/(1+cos(ax+b)) dx
2:01

trig integral ∫1/(1+cos(ax+b)) dx

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exp integral ∫ (e^2x -1) /(e^2x +1)dx
2:16

exp integral ∫ (e^2x -1) /(e^2x +1)dx

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UC Davis #13: integrate ∫(x+3)(x-1)^5 dx
1:35

UC Davis #13: integrate ∫(x+3)(x-1)^5 dx

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3rd/4ways: trig derivative sin(x)
1:30

3rd/4ways: trig derivative sin(x)

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1st way: STPM Math T Sem2 By using the Maclaurin's theorem show that ...
9:15

1st way: STPM Math T Sem2 By using the Maclaurin's theorem show that ...

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COMMON MISTAKE: (1) logb(m) logb(n) ≠ logb(m+n)
2:05

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

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