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

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2nd way: integral ∫ log √x(x^n) dx

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

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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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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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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.
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1st/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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Alternate way: integral ∫ax+b dx
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Alternate way: integral ∫ax+b dx

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2 ways: sq root √x^x
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2 ways: sq root √x^x

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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)
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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)

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commutative: ab=ba via "picture"
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commutative: ab=ba via "picture"

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exp derivative e^(ax+b)/2^(ax)
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exp derivative e^(ax+b)/2^(ax)

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)
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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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2 ways: derivative (ax+b)^n
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2 ways: derivative (ax+b)^n

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Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx
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Princeton U: Compute the integral ∫sin^5(x)/cos(x) dx

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx
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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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Evaluate these 7 integrals ...
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Evaluate these 7 integrals ...

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trig integral ∫1/(4-3cos^2(x)+5sin^2(x)) dx
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trig integral ∫1/(4-3cos^2(x)+5sin^2(x)) dx

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