Expert: Paul Klarreich - 5/12/2007

Question
I am studying for my A level maths exam this month and have come across a past-paper question that doesn't seem to work:
Q) "Use Integration by Parts to evaluate the integral of ln(1+x)dx "

I would appreciate an explanation of how to get the answer so I can do this in my exam
Thanks for your help.


Answer
Questioner:   Simon
Category:  Advanced Math
 
Subject:  Integrating by Parts question
Question:  I am studying for my A level maths exam this month and have come across a past-paper question that doesn't seem to work:
Q) "Use Integration by Parts to evaluate the integral of ln(1+x)dx "

I would appreciate an explanation of how to get the answer so I can do this in my exam
Thanks for your help.
................................
Hi, Simon,

This integral:

{
| ln x dx  
}

is one of your standard IBP exercises:

u = ln x,   du = 1/x dx
dv = dx,  v = x

Integral becomes:
        {
x ln x - | dx
        }
and the rest is easy.

Now about your:

{
| ln(1 + x) dx
}
Do this change of variable:

y = 1 + x,  dy = dx

and you have:

{
| ln y dy
}
Now do it as above.