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trig integral Find cos^2(x) sin(x) dx

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2 ways: integral ∫(x-a)/(x+a) dx
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2 ways: integral ∫(x-a)/(x+a) dx

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

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

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Swinburne U 2nd way: e^(-e^x) e^x dx
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Swinburne U 2nd way: e^(-e^x) e^x dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 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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Review: Linear form, Quadratic form & Bilinear form

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...
1:23

A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)
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trig Show sec^4(x)-tan^4(x) = sec^2(x)+tan^2(x)

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Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]
3:51

Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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Screen Recording 2024-05-19 at 9.45.17 PM
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Screen Recording 2024-05-19 at 9.45.17 PM

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trig Show 1/(1-sin(x)) + 1/(1+sin(x)) = 2 sec^2(x)
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trig Show 1/(1-sin(x)) + 1/(1+sin(x)) = 2 sec^2(x)

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2nd Alternate trig ∫integral sin(x) dx
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2nd Alternate trig ∫integral sin(x) dx

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

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

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2nd way: derivative x^n w.r.t x^x
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2nd way: derivative x^n w.r.t x^x

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Pascal's triangle rCk [examples]
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Pascal's triangle rCk [examples]

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2nd way: derivative (a-bx)^(px-q)
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2nd way: derivative (a-bx)^(px-q)

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1st/2ways: r-Permutations
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1st/2ways: r-Permutations

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"
8:49

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

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