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logic: Show p→q ≡¬ p∨q
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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 way: exp ∫(e^x)/x (1+x log(x)) dx
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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx
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2nd way: integral ∫ log √x(x^n) dx
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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx
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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx
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derivative (f(x))^n vs n^(g(x)) vs (f(x))^g(x)
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picture "proof":Show Σk^2 = ΣΣmin(i,j) where i,j,k=1 to n
2nd way: derivative ∫log (f(x))^g(x) (p(x))^r(x)
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logic Show by truth table x∧(x→y)→y is Tautology
implicit differentiation Find dy/dx, sin(xy) +x/y = x^2 -y
2nd way: integral tan(x)/(1+tan(x)) dx
#17 2022 MIT Integration Bee Qualifying Exam
Screen Recording 2023-11-24 at 12.00.30 AM
Fill in each blank using either mean or median.
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exp integral ∫1/(e^(2x) - 25) dx
#6 2014 MIT Integration Bee Qualifying Exam
#8 Lamar U: evaluate integral sec^8(t/2) tan^5(t/2) dt
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