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Path to USA Green Card for Exceptional Talent
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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx
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exp Calculate ∫x^3 3^x dx via IBP
#1 2017 MIT Integration Bee Qualifying Exam
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#12 2024 MIT Integration Bee Qualifying Exam
The prob. density function of a r.v X is given by the formula
2nd way: integral ∫p^(nx) q^x dx
Show ∫f'(ax+b) dx = f(ax+b)/a + C
Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5
multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.
U Penn: Show that the following decomposition CANNOT hold ...
#2 2024 2nd/2 ways: MIT Integration Bee Qualifying Exam
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UC Davis #8: integral cos(5x)/(3+sin(5x)) dx
prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.