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2nd/2 ways: trig integral sin(x)/x + cos(x)/x^2 dx

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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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Alternate way: Find 1+2+3+... +(n-1)+n via "polynomial degree 2"

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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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2nd way: derivative (x^x)^x
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2nd way: derivative (x^x)^x

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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STPM Math T Sem. 2: Ex 11.2 Given that f(x)=tan(x), show that ...

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2nd/2 way: Expand e^sin(x) by Maclaurin's Theorem
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2nd/2 way: Expand e^sin(x) by Maclaurin's Theorem

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1st way: count values nPn, nP(n-1), nP(n-2)
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1st way: count values nPn, nP(n-1), nP(n-2)

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prob stat: x̄=∑xk where k=1,2,3,...,n?

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count Show Σ k^2 = ΣΣmin(i,j) where i,j,k=1 to n
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count Show Σ k^2 = ΣΣmin(i,j) where i,j,k=1 to n

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2 ways: Σ 1? where k=m to n

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

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2nd way: If y=(ax-b)/(a-bx), prove that 2y1y3=3(y2)^2
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2nd way: If y=(ax-b)/(a-bx), prove that 2y1y3=3(y2)^2

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2nd way: integral ∫x/(2ax-x^2) dx
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2nd way: integral ∫x/(2ax-x^2) dx

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