1. ## Definite integral

Hi,

I am working on the following problem:

write (4x-3)/(2x+1) in the form A + B/(2x+1) and evaluate the integral of (4x-3)/(2x+1)dx from x=0 to x=2

I haven't seen a question like this before and don't really know how to solve it... I did some reading around about partial fractions in integration but I am stuck. Any help would be appreciated, thank you.

Andy

2. ## Re: Definite integral

Originally Posted by andy000
Hi,

I am working on the following problem:

write (4x-3)/(2x+1) in the form A + B/(2x+1) and evaluate the integral of (4x-3)/(2x+1)dx from x=0 to x=2

I haven't seen a question like this before and don't really know how to solve it... I did some reading around about partial fractions in integration but I am stuck. Any help would be appreciated, thank you.

Andy
This isn't really a partial fractions problem. Those generally involve a product of terms in the denominator.

What you can do on this problem as you've noted is that it can be rewritten as

$\dfrac {4x-3}{2x+1} = \dfrac{2(2x+1)-5}{2x+1}=2-\dfrac{7}{2x+1}$

which is easier to integrate.

3. ## Re: Definite integral

Oh thanks romsek, I will go from there.

Cheers

4. ## Re: Definite integral

Oh sorry, should that be -5 instead of -7?