Gurjat CET-2007 2nd way log exp ∫e^(xln(2006) e^x dx

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

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

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

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2nd way: integral ∫ log √x(x^n) dx

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1st way: exp ∫(e^x)/x (1+x log(x)) dx

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The number of solutions of the equation x^(log10(x)) = 100x

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Review: integral ∫1/(x^2-a^2)dx vs integral ∫1/(a^2-x^2) dx vs integral ∫1/(x^2+a^2) dx

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Alternate way: derivative If y=e^(a arc sin(x)), prove that (1-x^2)y2-xy1=a^2y

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logic implication distribute across disjunction: Show x→(y∨z) ≡ (x→y) ∨ (x→z)

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

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2nd way: trig integral (3-tan^2(x))/(cot(x)-3tan(x)) dx

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2nd way: trig integral ∫cos(x)/(sin^2(x) + 4sin(x)+3) dx

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2nd way: exp integral ∫2^(5x) 3^(-x) dx

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Which pairs are equivalent via truth table?

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2nd way: integral ∫x^2 √(x^3+1) dx vs ∫x^3 √(x^3+1) dx

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2nd way: exp integral ∫e^(a√x)/√x dx

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

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2nd way: integral ∫x^k ln(x) dx = x^(k+1)/(k+1) ln(x) - x^(k+1)/(k+1)^2 + C where C ≠ -1

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#1 2024 MIT Integration Bee Qualifying Exam

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Screen Recording 2024-05-19 at 9.56.54 PM

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