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

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Math Lover

Posts: 65
Registered: 4/9/14
Re: Compute integral
Posted: May 2, 2014 2:38 AM
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In article <7a15bcf9-f4b5-46a1-88cf-438a1434929b@googlegroups.com>,
<cootercrew@gmail.com> wrote:

> Compute the integral from 0 to 1 of ln(1+x)/(1+x^2)dx. Hint: Use the
> substitution y+1=2/(x+1)


Just to be sure: do you mean

ln(1+x)
-------
1+x^2

Or

ln( (1+x)/(1+x^2) )?

The first one does not seem to evaluate to closed form, the second
one is standard: write as ln(1+x) - ln(1+x^2) and do them by
parts, using the trick int(f) = x*f - int(x*f'). Works here since
the f' terms have no "ln" in them and in both case x*f' is trivial
to integrate.

Cheers, L.




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