Hi, I needed help with this improper integral.

Question

lower limit : 2
upper limit : infinity

integral of (lnx)/(x+1) dx

Thank You so much :D

Answer 1

I saw this question and have not been able to get a handle on it

we know that ln(x) has an expansion formula
http://upload.wikimedia.org/math/6/d/b/6dbf56b2e5f34d298c1e71ddd93b3448.png

but it only good for |x-1| < 1

so we could create a series of terms
= 1/(x+1) ( (x-1) - (x-1)^2 /2 + (x-1)^3 / 3 - .... )

but to integrate each term would be a mess
- even Wolfram, usually very dependable, could not handle it.

http://integrals.wolfram.com/index.jsp?expr=ln%28x%29%2F%28x%2B1%29&random=false