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

3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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

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2nd way: integral ∫ log √x(x^n) dx

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

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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derivative log f(g(x)) (p(r(x)))

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Common log mistake: logb(xy^n) ≠ nlogb(xy)

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examples 2x2 matrix withOUT an inverse

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3rd/3 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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

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Find the number of subsets of {0,{0},{{0}},{{{0}}}}

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2nd way: trig inverse ∫(2012)^x (2012)^ arc (sin(2012)^x)√(1-(2012)^2x) dx

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

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2 ways: derivative a^f(g(x))

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2nd/2 ways: Alternate way: Given 2 points, find equation of st line passing the ..

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2 ways: trig integral ∫ sec^2(x) csc^2(x) dx

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2 ways: exp integral ∫(p^x + q^x)/r^x dx

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1st/2ways: Evaluate trig integral ∫1/(sin(x)+cos(x)) dx

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logic: tautology p→q≡(¬q→¬p)

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