3 ways: rational function integral ∫(x^2+1)/(x-1)^3 dx

2 ways: integral (3+5x)/(x(x-1)) 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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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(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/2 way: Expand e^sin(x) by Maclaurin's Theorem

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1st/2ways: Taylor series of cos(x)

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2nd/2 parts: Mean 1+2+3+...+n is just (1+n)/2. Why?

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We lost original x's but still know mean x̄ & n. Now we collected m new observations.

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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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/2ways: Find lim (z^3-8)/(z-2) for z tends to 2

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2nd/3 ways: How many chords can be drawn through 21 points on a circle?

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derivative: If x=cos(log(y)), show that (1-x^2)y2 - xy1 = y

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exp integral ∫1/(e^(ax+b) (1+e^(ax+b)) dx

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

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Solve cos^2(x) dy/dx +y = tan(x) via Integrating factor[IF]

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exp integral e^x (f(x) + f'(x)) dx

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