If xy+y^2=tan(x)+y,then find dy/dx

Diff Eq: Solve sec(x) dy/dx=y+sin(x) via Integrating factor [IF]

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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

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3rd/3 ways: Express (4x-17)/((x+4)(2x-3)) in partial fractions via withOUT cover rule

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1st/2ways: r-Permutations

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1st way: Differentiate the function w.r.t x log10(x)+logx(10)+logx(x)+log10(10)

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#16 MIT 2022 Integration Bee Qualifying Exam

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Always ZERO

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2nd way: Evaluate integral ∫x^2/√(19-x^2) dx

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logic: contradiction p∧¬p

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sq root integral ∫1/√...√√x dx with n √

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1st/2 ways: derivative y=(ln(x))^x

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2 ways: diff eq Solve dy/dx=y-1

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trig integral ∫sin^(-2/3)(x) cos^3(x) dx

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1st/2ways: exp e^g(x) (g'(x)f(x) + f'(x)) dx

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3 ways: exp trig Differentiate the function a^sin(√x)

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2nd way: derivative y=e^x sin(x) cos^3(x)

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exp trig derivative x^x sin(x)

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