Is there any way to write 2/3ln(x-1/x=1) as ln(x-1/x+1)^3/2? My answer for an integral problem was the 1st mentioned answer and trying to see if I just missed log properties of writing the answer a different way.

Question

hartnn · Answer

$\huge a\log b = \log b^a$

hartnn · Answer

so you should have got 
3/2 ln (x-1/x+1)

anonymous · Answer

Maybe I had an error in my calculations. Can you check a partial fraction integral with me if I show you what I did?

hartnn · Answer

ofcourse :)

hartnn · Answer

post original Question also

anonymous · Answer

$$\int\limits 3/x^2-1 dx$$

$$3/(x-1)(x+1)=A/x+1 + B/x-1$$

anonymous · Answer

can I skip ahead to my partial fractions?

hartnn · Answer

yes, what u got as A , B ?

anonymous · Answer

A= -2/3
B=2/3

hartnn · Answer

correct :)

anonymous · Answer

So...
$$\int\limits -2/3/(x+1) dx + \int\limits 2/3 (x-1) dx$$

hartnn · Answer

oh wait!

hartnn · Answer

A= -3/2
B = 3/2

hartnn · Answer

3 = A(x-1) +B(x+1)
right ?

anonymous · Answer

yes

hartnn · Answer

if you put x=1 here, u get 
3 = B (2)
B=3/2
:)

anonymous · Answer

let me check that out (;

anonymous · Answer

Awesome!! Thank you so much for your help (; What school do you go to?

hartnn · Answer

i completed my education this year :)

anonymous · Answer

In math?

hartnn · Answer

nopes, in Telecommunication system Engineering, but it had good amount of math too :)

anonymous · Answer

Have you found a good job since getting out of school? Im working on EE

hartnn · Answer

yes, i did! i work in Cisco Systems as software engineer.
but i live in India, the situation in your country might be completely different...

anonymous · Answer

Thats great! I live in U.S. 
One last question about partial fractions...m just starting ot do these problems and have been wondering if it matters which factor such as (x-1) (x+1) I use as denominator of A and B?

hartnn · Answer

no it does not matter. 
you will just get different (exchanged) values of A,B but your final answer will be same :)

anonymous · Answer

Thank you so much I really appreciate your help. Do you come on here to practice your math skills?

hartnn · Answer

you're welcome ^_^
i come here mostly to help people with their math, i like helping, and math :)

anonymous · Answer

Thanks again (;