I want to integrate ln(x/(x-2a)) from 3a to 4a. I split it up into two integrals to integrate now [lnx - ln(x-2a)] from 3a to 4a but somehow this seems not to work out. Why can't I split this term to make it easier? (a is positive number so there is not a negative number in the ln so I should be allowed to split it up).

Question

anonymous · Answer

The answer should be a*ln(64/27) or 3aln(4/3) but I always end up with ln(2/3)...
Everytime I end up with 4aln4a-2aln2a-3aln3a+alna...

dumbcow · Answer

ok i worked it out by splitting the log and got the correct answer
take what you ended up with and continue to simplify by splitting up the logs
ln(4a) = ln(2a) +ln(2)
ln(3a) = ln(a)+ln(3)
ln(2a) = ln(a)+ln(2)

anonymous · Answer

Thx a lot dumbcow. I wrote everything in one big log -> (4a^4a*a^a/2a^2a*3a^3a) and wrote that as 2/3 - I guess than there must be my mistake.

dumbcow · Answer

oh wow, yeah you can make it easier on yourself and just break it down to just terms of ln(a)

anonymous · Answer

but that big log does not give me the answer I want :(

anonymous · Answer

That is one hell of an integral... but now I finally got it. :) One of those cases where making the term larger by splitting the ln up makes it "easier" instead of writing one big ln.