1. ## [SOLVED] Integration problem

Hi guys,

I need to integrate the following equation with respect to x.

$\displaystyle -ax + \frac{ab}{c-x}$

where a,b and c are integers. I was advised to re-write the equation as

$\displaystyle -ax -ab\frac{-1}{c-x}$

and i'm pretty confident in integrating the first part of the equation, but i dont know how to integrate the last part. I'm guessing that the answer will involve ln(?) but i dont know how to work out what its meant to be the log of, so if anybody could help me i will be truely thankful as i've been trying to work this out for a while, getting nowhere!

2. Originally Posted by Kimmy4
Hi guys,

I need to integrate the following equation with respect to x.

$\displaystyle -ax + \frac{ab}{c-x}$

where a,b and c are integers. I was advised to re-write the equation as

$\displaystyle -ax -ab\frac{-1}{c-x}$

and i'm pretty confident in integrating the first part of the equation, but i dont know how to integrate the last part. I'm guessing that the answer will involve ln(?) but i dont know how to work out what its meant to be the log of, so if anybody could help me i will be truely thankful as i've been trying to work this out for a while, getting nowhere!

Note that $\displaystyle \frac{-1}{c-x} = \frac{1}{x-c}$ and the antiderivative of $\displaystyle \frac{1}{x-c}$ is $\displaystyle \ln{|x-c|}$.

3. Wow is it really that simple! I was thinking it was gonna be much more complicated than that! Thanks.

so am i right in saying that the whole integral is

$\displaystyle \frac{-ax^2}{2} - abln(x-c)$

Thanks again

4. Originally Posted by Kimmy4
Wow is it really that simple! I was thinking it was gonna be much more complicated than that! Thanks.

so am i right in saying that the whole integral is

$\displaystyle \frac{-ax^2}{2} - abln(x-c)$

Thanks again
Yes, that is the correct integral. Don't forget to add your constant.