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KS 66
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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) 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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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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1st way: exp ∫(e^x)/x (1+x log(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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partial Let f(x,y,z)=x e^(yz). Compute fxzy & fyxz.
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#19 2011 MIT Integration Bee Qualifying Exam
Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)
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Lamar U 2nd way: evaluate integral ∫1/(3x) + sec(9x)tan(9x)e^sec(9x) dx
#9 2010 MIT Integration Bee Qualifying Exam
multivariable partial Let w=2x^2 y, where x=u^2+v^2 & y=u^2-v^2. Find ∂w/∂u & ∂w/∂v.
Lamar U 2nd way: evaluate trig log sq rt integral ∫sin(1+ln(2x))-√(1+ln(2x))/x dx
#18 2010 MIT Integration Bee Qualifying Exam
Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5
Find the number of digits in a number? (118^118)
#17 2011 MIT Integration Bee Qualifying Exam
NONelementary integral ∫e^(ax)/x dx
#8 2014 MIT Integration Bee Qualifying Exam