1. ## Complex values

I am obviously ignorant of this topic but I was fiddling and

the real part of some complex integrals resembel their actual integral?

What is the correlation

$\displaystyle Re\bigg[\int[\ln(x+i)+\ln(x-i)]\bigg]dx$
Resembles $\displaystyle \int\ln(x^2+1)dx$

Is this just conicidence?

2. Originally Posted by Mathstud28
I am obviously ignorant of this topic but I was fiddling and

the real part of some complex integrals resembel their actual integral?

What is the correlation

$\displaystyle Re\bigg[\int[\ln(x+i)+\ln(x-i)]\bigg]dx$
Resembles $\displaystyle \int\ln(x^2+1)dx$

Is this just conicidence?
From the rules of logarithms
$\displaystyle ln(x + i) + ln(x - i) = ln((x + i)(x - i)) = ln(x^2 + 1)$

so the two had better not only "resemble" each other, they had better be the same!

-Dan

3. Originally Posted by topsquark
From the rules of logarithms
$\displaystyle ln(x + i) + ln(x - i) = ln((x + i)(x - i)) = ln(x^2 + 1)$

so the two had better not only "resemble" each other, they had better be the same!

-Dan
Yeah I know that...that is what I meant when I said "fiddling" I was doing that integral and I didnt want to do sub and then parts so I said I wonder if taking the real part of the sperated log is the same?