exp integral ∫e^x /(e^2x + 4) dx

MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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🪔 Happy Deepavali 🪔 [Nov-12-2023]

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

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

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2nd way: derivative (x^x)^x

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

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2 ways: ¬p→q ≡ p∨q

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2 ways: exp derivative ln(e^(x+1/x))

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4th/5ways: triangular num: Show t(n-1) + tn = n^2 where tn = nth triangular number

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2nd/3part: Maclaurin Series [ahp kia]

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alternate way: count sum 1 + 2 + 3+... + n via "polynomial"

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Quickie: 6169^2 - 2331^2?

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1) integral ∫ 1/(1+x^2) dx 2) integral ∫ e^x/(1+e^(2x)) dx 3) integral ∫ cos(x)/(1+sin^2(x)) dx

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Growing patterns #3

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AP Calculus: integral ∫(5√x^3 + √6x) /√x dx

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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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Solve x(x-1)dy/dx - (x-2)y=x^3(2x-1) via Integrating Facto[IF]

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

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4 ways: Evaluate Σ(2k+1) k=1,20

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

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