Show integral 1/(x(x^2+a^2)) dx = 1/(2a^2) ln(x^2/(x^2+a^2))

logic Idempotent law show x=xVx

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

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

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(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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Pantun Melayu [Buah cempedak di luar pagar]

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Pantun Melayu [Sorong papan tarik papan]

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Lamar U 2nd way: evaluate trig integral ∫17(xe^x+e^x)sin(e^x)-14sin(x) dx

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#9 2010 MIT Integration Bee Qualifying Exam

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#2 2011 MIT Integration Bee Qualifying Exam

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alternate way: ∫ √(x^2+a^2 )dx via "expressing in 2 ways"

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#19 2011 MIT Integration Bee Qualifying Exam

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If u=a+ib is a complex #, then complex conjugate of u*=a-ib. ...

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2nd way: trig integral ∫1/(a+b sin(x)+c cos(x)) dx

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The prob. density function of a r.v X is given by the formula

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Lamar U 2nd way: evaluate exp integral ∫e^(8x)(4+e^(4x))^(-3) 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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2nd way: integral ∫x^2 √(x^3+1) dx vs ∫x^3 √(x^3+1) dx

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