NUS MA1102R: For f(x,y) = e^(xy) + x/y, compute fx & fy

Differentiate x/sin(x) w.r.t. sin(x)

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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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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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2nd way: integral ∫ log √x(x^n) dx

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trig Write each expression as an equivalent algebraic expression involving only x.

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If y=acos(ln(x)) + bsin(ln(x)), show that x^2y2 + xy1 +y=0

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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)

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

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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n

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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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UC Davis#4 4 ways: integrate 7^(2x+3) dx

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Screen Recording 2023-12-02 at 3.42.17 AM

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

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Review Add Math: Show a^m a^n = a^(m+n) where m & n are any 2 positive integers

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integral sin(x)/(1+sin(x)) dx

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2nd/2 ways: #1 2019 MIT Integration Bee Final

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2nd way: trig Evaluate 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫ sin^3(x)/√cos(x) dx

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#17 2022 MIT Integration Bee Qualifying Exam

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