# Integration by parts question

1. Feb 20, 2008

### Monocles

[SOLVED] integration by parts question

1. The problem statement, all variables and given/known data
This is part of a larger problem but I'm just not sure if I have the right answer.

edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex

2. Relevant equations

3. The attempt at a solution
u-substituion:

$$u = x - 7$$

$$du = dx$$

Integration by parts to get

$$\intlnudu = ulnu - \int1du$$

$$= ulnu - u$$

$$= (x - 7)ln(x - 7) - (y - 7) + C$$

Now my only problem with this answer is that it gives 7 + C as part of the answer, and I can't recall ever seeing a constant + C as the answer for any integral.

I actually plugged the equation into this integral finder:

http://integrals.wolfram.com/index.jsp

And it told me that it was

$$(x-7)ln(x-7) - x$$

I'm guessing the +C is a given.

I would just leave it at +C and go on but its part of a differential equation so the value of C ends up being important...

Last edited: Feb 20, 2008
2. Feb 20, 2008

### Dick

C is not just a constant in the integration. It's an ARBITRARY constant. There is no difference between C and C+7. Just leave it at C and go on.

3. Feb 20, 2008

### Monocles

Alright thanks :)

4. Feb 20, 2008

### Mindscrape

You mean x-7 and a constant plus a constant is a constant. Both you and mathematica have the right answer, but mathematica just absorbed the 7 into the constant. Differentiate it to check. :)