# Thread: definite integral (logarithmic) completely lost

1. ## definite integral (logarithmic) completely lost

problem:

Integrate (2x-1)/(x+1) from 0 to 3

the first thing I do is pull out the constant 2. Then the part to integrate can become ln(x-1)-ln(x+1)

the antiderivative of ln(x-1) is:
x(ln(x-1)-1)-ln(1-x)

the antiderivative of ln(x+1) is:
(x+1)ln(x+1)-x

x(ln(x-1)-1)-ln(1-x)-(x+1)ln(x+1)-x

3(ln(3-1)-1)-ln(1-3)-(3+1)ln(3+1)-x

I can already tell this answer is wrong due to the fact that I have negatives in the ln

the final answer should be 6(1-ln2)

any help?

2. ## Re: definite integral (logarithmic) completely lost

Originally Posted by NecroWinter
Then the part to integrate can become ln(x-1)-ln(x+1)
How? I've no idea how you have arrived at this step.

To do your integral note (2x-1)/(x+1) = 2-[3/(x+1)].

3. ## Re: definite integral (logarithmic) completely lost

Originally Posted by TheSaviour
How? I've no idea how you have arrived at this step.

To do your integral note (2x-1)/(x+1) = 2-[3/(x+1)].
its possible I confused the property of logarithms.

Anyway, how do you go from (2x-1)/(x+1) to 2-[3/(x+1)]

4. ## Re: definite integral (logarithmic) completely lost

[(2x-1)/(x+1)] =[(2x+2-3)/(x+1)] = [2(x+1)-3]/(x+1) = 2(x+1)/(x+1)-[3/(x+1)] = 2-[3/(x+1)].