Review: Product to Sum Identities

2nd/3 parts: Growing patterns

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2nd way: integral ∫ log √x(x^n) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(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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Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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3rd/3 parts: Growing patterns

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NUS MA1102R: Find ALL second-order partial derivatives of f(x,y) = x^2 y -y^3 + ln(x)

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2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫x^5 √(1+x^3) dx

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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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3rd/3part: Maclaurin Series [ahp kia]

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sum: Find a close formula for 2,3,14,24,37,...

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Matriculation & Calculus: Show if y=f(x) g(x) h(x) k(x)

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integral ∫x^2/√(x^2+a^2) dx

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Alternate way: Derivative y=ln((x^4-8)^5/(x^6+5x)cos(x))

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AP Calculus: integral ∫ln(a+bx^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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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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A bag contains 20 identical red marbles, 20 identical green marbles, & 20 identical blue marbles.

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