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derivative If y=(a+bx)e^(-nx), prove that y2+2ny1+n^2y=0
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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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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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2nd way: integral ∫ log √x(x^n) dx
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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"
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prob stat: Consider the experiment of tossing a fair coin twice & reading the up face on each toss.
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2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2
Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx
MIT Integration Bee Qual. Exam #1: integral x^(1/log(x)) dx
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Fill in each blank using either mean or median.
STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)
NONelementary integral ∫e^(ax)/x dx
Find the equation of the tangent line to the curve x^3-3y^3+xy+21=0 at the point (1,2)
MIT Integration Bee Qual. Exam #9: integral (2logx+1)e^(log(x))^2 dx
2nd/2 ways: derivative x^2/3 + y^2/3 = a^2/3
2nd way: ∫1/(√x cos(√x)) dx
Lamar U: Use log. differentiation to find the 1st derivative of the given function
Solve the differential equation xcos^2(y) dx + tan(y) dy=0