Show log b^n(x^m) = m/n logb(x)

Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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2 ways: sq root derivative 1/(√√(1/√x))

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2nd way: integral ∫ log √x(x^n) dx

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naruto

Jeffrey Mijares Gali

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

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2nd/2 parts: sum Find the sum 2,3,14,24,37,... nth term

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2024 #3 MIT Integration Bee Final Lightning Round

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Sum of Square vs Square of Sum

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3 picture views of the sum ... 1+2+3+...+n

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3 ways: derivative e^y=x

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Review: Product to Sum Identities

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4 ways: sum Find the sum of the values of 4+3i for i=1,2,...,100

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AP Calculus 2nd way: trig integral ∫sin^2(x) cos^2(x) dx

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2 ways: Derivative √ (1+√ (1+√ x)))

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1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number

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2nd way: integral ∫(6+4x--2x^2) dx via 1) complete sq 2) then trig. sub

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AP Calculus 2nd way trig integral ∫x^2 cos(x) dx

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diff eq: Solve dy/dx = (2y4x^4)/(xy^3) ❌separable to ✅separable

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2nd/2ways: trig Evaluate (sin^6(x) + cos^6(x))/(sin^2(x) cos^2(x)) dx

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