2nd/2 ways: FInd partial fractions (3x^2+9x-20)/(x^2+x-6)

2nd/3 parts: Growing patterns

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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2nd way: integral ∫ log √x(x^n) 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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integral ∫x^2/√(x^2+a^2) dx

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3rd/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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sum picture proof show 1^2+2^2+3^2+...+n^n=1/3 1/2n(1+n) (2n+1)

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Derivative 1) tanh(ln(x)) 2) (x^2-1)/(x^2+1)

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A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.

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Prove Σ1/((k-1)(k+1))=(3n^2-n-2)/(4n(n+1)) where k=2 to n ∀n ≥ 2

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1st/3ways: derivative (x+1)^(1/2) (x+2)^(1/3) (x+3)^(1/4) (x+4)^(1/5) (x+5)^(1/6)

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prob stat: 2 ways The mean of five #s 2,3,5,6,8 is 4.8. Calculate the std deviation.

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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Integrate ∫x^3 sin(arc tan(x^4))/(1+x^8) dx

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5 ways: trig Derivative of sin^2(x)

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Florida International U: Find derivatives ...defined implicitly ... (a)-(c)

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trig integral a) ∫csc^2(x) dx

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1st/2ways: Evaluate lim sin(5x)/sin(9x) as x tends 0

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