Columbia U: 10th/10 ways Evaluate the indefinite integral ∫1/(1+e^x) dx withOUt u-sub

Compute the arithmetic mean for the following grouped data ...

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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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2nd/3ways: trig integral ∫sec(x) dx

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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integral ∫ x dx withOUT using Power rule.

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2nd way: derivative (x^x)^x

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Penn. State U: Suppose the p.m.f of discrete random variable X is ...

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example: Mean, Median & Mode

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8Screen Recording 2023-12-07 at 1.55.57 AM

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2nd way: integral ∫1/x log mb(x) dx

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8Screen Recording 2023-12-07 at 1.55.57 AM

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2nd way: trig integral ∫ tan(x)/(tan^2(x)+tan(x)+1) dx

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Find the expected value & the variance of a geometric r.v. X

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trig integral ∫x/(1+x) dx vs ∫cos(x)/(1+cos(x)) dx

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IIT-1995 2nd way integral ∫x^5/(1+x^3) dx

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2nd way: log sqr integral ∫ln(x)/x dx

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Lamar U #12 trig integral sec^4(2t)/tan^9(2t) dt

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2nd way: sq rt integral ∫(√x)/(x+1) dx

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2nd way: derivative (x/a)^n/(n-1) + (y/b)^n/(n-1) = 1

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