Easy integration by parts help

1. Sep 18, 2010

MillerGenuine

1. The problem statement, all variables and given/known data

integral of ln(2x +1)

2. Relevant equations
I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit. im not sure what it is the ln of.

3. The attempt at a solution

U= 2x+1 dV= lnU (?)
dU/2= dx V= 1/U (?)

2. Sep 18, 2010

ehild

When you want to integrate by parts, a good choice for u is that part which has a simple derivative, and for v that part which is easy to integrate. So you can choose ln(2x+1)=u and 1=dv/dx

ehild

3. Sep 18, 2010

MillerGenuine

ok perfect. got the answer. I have seen it done the way you just showed & i have also seen it done a different way. If we first substitute
p= 2x+1
dp/2 = dx
then once this is done we have 2 integral ln(p).
now from here we do integration by parts by choosing
u= ln(p) dV= dp
du= 1/p V= p

now is there any difference between the two? or any situations where one will work and the other wont?

4. Sep 19, 2010

ehild

Both methods have the same result, but substituting first 2x+1 by p is much simpler. Do not forget to plug in 2x+1 for p at the end.

ehild