inverse trig integral ∫x arc sec(x^2)/(x^2 √(x^2-1)) dx

2nd/2 way: Expand e^sin(x) by Maclaurin's Theorem

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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/2ways: Find the sum 1/7, 10/21, 17/21, 24/21, 31/21 via median.

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logic Idempotent law show x=xVx

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2nd way: integral ∫ log √x(x^n) dx

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

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

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2nd way: sq rt log integral ∫√√√(x) ln(x) dx

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Example: Find the sum

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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trig integral ∫1/(√sin(x) √cos^7(x)) dx

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integral ∫(x^2+2x)/(x^2+2x+2) dx

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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integration bee 2014 UNSW: 4th way: e^x(cos(x)+sin(x)) dx

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

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

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Screen Recording 2024-02-18 at 12.10.36 AM

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3 ways: derivative log(x+ (1+√(x^2)))

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impIicit diff f x^y=y^x, find dy/dx at (2,4)

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integral ∫x^3/(x+2) dx

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