2 ways: derivative ln(ax-b)^(p-qx)

Show ∫ f'(x)/√f(x) dx = 2 √f(x) + C

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

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logic Idempotent law show x=xVx

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

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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Alternate way: inverse trig integral ∫e^(m arc tan(x))/(1+x^2) dx

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Suppose z is differentiable funtion of x & y that is defined implicitly x^2+y^3-z+2yz^2=5

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2nd/4ways: trig derivative sin(x)

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1Screen Recording 2024-05-17 at 6.16.11 PM

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log integral ∫(ln(x))^m/x dx

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integral ∫x^3/(1-x^8) dx

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2nd way: trig integral ∫1/(cos^2(x) - sin^2(x)) dx

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U North Texas Integration Bee 2nd way: x^2/√(x-1) dx

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trig integral ∫sin(2x) cos(2x) / (9-cos^4(2x)) dx

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Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

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AP Calculus 2nd way: integral ∫1/(3√(x^2) + 3√(x^4)) dx

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

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2nd way: integral ∫x^2 (x+1)^9 dx via withOUT u-sub

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Screen Recording 2023-12-06 at 3.09.43 AM

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