Show integral 1/(x^2(x^2+a^2)) dx = -1/(a^2x) - 1/a^3 arc tan(x/a)

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

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prob stat The prob of events A & B are P(A) & P(B) respectively P(A)=5/12, P(A n B)=1/6, P(AuB)=q.

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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2nd/3ways: trig integral ∫sec(x) dx

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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2nd way: integral ∫ log √x(x^n) dx

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2 ways: sq root derivative 1/(√√(1/√x))

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Columbia U: 4th/6 ways Evaluate the indefinite integral ∫1/(1+e^x) dx

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Screen Recording 2024-05-05 at 11.26.15 PM

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NDA-2004 2nd way integral ∫(x-x^3)^1/3/x^4 dx

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1st/2 ways: integral ∫1/(x(x^n -1)) dx

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2nd way: exp integral ∫(e^(-x) - e^x)/(e^(2x) + e^(-2x) 2) dx

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Screen Recording 2024-05-05 at 11.28.23 PM

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Columbia U: 2nd way Evaluate the indefinite integral ∫1/(1+e^x) dx

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Screen Recording 2024-05-19 at 11.13.23 PM

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Screen Recording 2024-02-02 at 1.54.05 AM

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Columbia U: 5th/6 ways Evaluate the indefinite integral ∫1/(1+e^x) dx

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2nd way: Evaluate ∫ 1/√(1-e^(2x)) dx

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

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