UT Austin: trig integral ∫(1-cos^2(x/2))^2 sin(x/2) dx

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Ruhul Amin_5968

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2nd way: integral ∫ log √x(x^n) dx

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

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

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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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1st/3parts: Checkpoint 1.1 STPM Math T Sem2

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

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Alternate way: exp derivative x^n

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logic: tautology p→q≡(¬q→¬p)

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2 ways: trig exp derivative e^(sin(x)) sin(e^x)

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

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2nd/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)

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Alternate way: trig integral ∫cos(x) dx

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2 ways: sq root √x^x

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Practice STPM Math Sem2 derivative

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1st/2parts: 2 (elementary) rules

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1st/3ways: derivative If f(x)=(x-a)(x-b)(x-c), show f'(x)/f(x)=1/(x-1)+1/(x-b)+1/(x-c)

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STPM Math T: trig double angle Express cos(2x) & sin(2x) in terms of tan(x)

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integral ∫(2x+3)/(4x^2+1) dx

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trig integral sin(tan(x)) cos(tan(x)) sec^2(x) dx [chain rule in reverse]

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