Columbia U: 2nd way integral Find ∫1/(x √(9-x^2)) dx withOUT trig-sub

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xauusd daily fibo analysis 8/6/2025 Sunday analysis

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2nd way: derivative x w.r.t x^x. [YES, d(x)/d(x^x)!]

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UC Davis: differentiate y=ln(cos^5(3x^4))

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

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2nd way: exp integral ∫x^x^2 x(2ln(x)+1) dx

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2nd way: trig integral ∫√(sec^5(x)/sin^3(x)) dx

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1st/2 ways[Direct]: Prove that the sum of 2 ODD numbers is ALWAYS EVEN

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A 2 digit number is equal to the sum of the product of its digits & the sum of its digits.

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2nd way: trig inverse ∫(2012)^x (2012)^ arc (sin(2012)^x)√(1-(2012)^2x) dx

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

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2nd way: exp integral e^g(x) (g'(x)f(x) + f'(x)) dx

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