Find the number of digits in mole [6.02x10^23]

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) 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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Screen Recording 2024-02-16 at 8.34.08 PM

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Screen Recording 2024-02-16 at 8.27.04 PM

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#3 2010 MIT Integration Bee Qualifying Exam

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4th/4parts: Maclaurin Series [ahp kia]

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trig integral ∫x^2 cos(x^3) e^sin(x^3) 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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prob stat: Two events are such that P(A)=0.6, P(B)=0.5 & P(AUB)=0.85

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#12 2024 MIT Integration Bee Qualifying Exam

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#8 2014 MIT Integration Bee Qualifying Exam

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2 ways: trig exp derivative e^(sin(x)) sin(e^x)

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2nd/2 ways: Show 1+3+5+ ... +(2n-1) + (2n+1) + (2n-1)+...+5+3+1= n^2 + (n+1)^2

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NONelementary integral ∫e^(ax)/x dx

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#12 2012 MIT Integration Bee Qualifying Exam

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3 ways: Find the first 3 terms of Maclaurin series for sin^2(x)

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derivative Find d2y/dx2 for this function y=ln(x)/(1-x)

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