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2nd/2 ways: MIT Integration Bee Final

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GPT4: A tweet snippet from Michal Kosinski

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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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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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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) 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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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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1st/3parts: Checkpoint 1.1 STPM Math T Sem2
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1st/3parts: Checkpoint 1.1 STPM Math T Sem2

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integral ∫ x dx withOUT using Power rule.
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integral ∫ x dx withOUT using Power rule.

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

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &
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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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Show that ar sinh(x) = ln(x + √ (x^2+1))
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Show that ar sinh(x) = ln(x + √ (x^2+1))

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exp integral e^2x/(1+e^x) dx
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exp integral e^2x/(1+e^x) dx

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example: Mean, Median & Mode
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example: Mean, Median & Mode

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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0
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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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3rd way: rational function integral ∫x^3/√ (1+x^2) dx
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3rd way: rational function integral ∫x^3/√ (1+x^2) dx

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log sq root integral ∫ln(√ x^3)/√ √ x dx
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log sq root integral ∫ln(√ x^3)/√ √ x dx

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2nd way: integral ∫1/(a + √√b (x^2)) dx
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2nd way: integral ∫1/(a + √√b (x^2)) dx

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Solve √(2x-5) -√(x-2) = 2

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4th/4ways: trig derivative sin(x)
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4th/4ways: trig derivative sin(x)

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sq root derivative √x [Good to know the result]
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sq root derivative √x [Good to know the result]

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