derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2 - xy1 = a^2y.

2nd way: derivative (x/a)^n/(n-1) + (y/b)^n/(n-1) = 1

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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 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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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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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2nd way: integral ∫ log √x(x^n) dx

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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2nd way: integral ∫log n√(ax+b)(ax+b) dxx

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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2nd way: ∫cos(x)/√(sin^2(x)+4sin(x)+3) dx

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2nd way: trig integral ∫sin(x/a) dx

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2nd way: trig log Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(x sin^2(1+log(x)) dx

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multivariable Let w=x^2y-xy^3 where x=cos(t) & y=e^t. Find dw/dt & its value when t=0.

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1st/2 parts stat: SLR SLR Regression lline always goes through the point (x̄, ȳ)

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A random variable X has the following parameters: E(X)=a & Var(X)=2a^2-1 a∈R

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2nd way: integral tan(x)/(1+tan(x)) dx

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2nd way: trig integral ∫1/(1+sin^2(x))cos^2(x))

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#16 2019 MIT Integration Bee Final

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