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Topic: Compute integral
Replies: 7   Last Post: May 2, 2014 1:36 PM

 Messages: [ Previous | Next ]
 Roland Franzius Posts: 586 Registered: 12/7/04
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

Date Subject Author
5/2/14 Jeremy Johnson
5/2/14 Math Lover
5/2/14 Roland Franzius
5/2/14 quasi
5/2/14 Jeremy Johnson
5/2/14 quasi
5/2/14 Peter Percival
5/2/14 Virgil