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Re: Compute integral
Posted:
May 2, 2014 3:23 AM


Am 02.05.2014 06:50, schrieb cootercrew@gmail.com: > Compute the integral from 0 to 1 of ln(1+x)/(1+x^2)dx. Hint: Use the > substitution y+1=2/(x+1) > > I'm pretty sure I need to get this in the form of the integral of ln > u du. So I use the substitution given and let u = 2/(x+1) but when > I compute the derivative of this I get [(x+1)*0  2(1)]/(1+x)^2 = 2 > /(1+x)^2 which does not equal 1/(1+x^2) like I need. I didnt get too > far trying integration by parts but maybe that is the way to go? I > doubt it because of the hint so pretty sure I am just missing > something getting it in the form of ln u du. > > Any help is appreciated! Thanks! This is just a practice problem for > a final and not something I have to turn in. >
Hint:
For
int_(0<x<1) dx/(1+x^2) log (1+x)
the substitution (Caley transform)
x > (1  y)/(1 + y)
generates the same integral with a negative sign
plus
Log 2 int_(0<x<1) dx/(1+x^2)

Roland Franzius



