Simple Integration using U Substitution

1. Jan 28, 2008

anon413

1. The problem statement, all variables and given/known data
Find the indefinite integral.
The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx

2. Relevant equations

3. The attempt at a solution

Tried using (x^2-1)^(1/2) as u and udu for dx and I solved for x but I am still left with a 1 on top not sure how to deal with it.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 28, 2008

rocomath

$$\int\frac{x^2-1}{\sqrt{2x-1}}dx$$

Yes?

Last edited: Jan 28, 2008
3. Jan 28, 2008

anon413

Sorry made a mistake in typing the denominator (2x-1)^(1/2) Im slightly displexic

4. Jan 28, 2008

anon413

How did you type that exactly.

5. Jan 28, 2008

rocomath

6. Jan 28, 2008

anon413

Yes thank you, that command latex is complicated I'll try to learn it.

7. Jan 28, 2008

sutupidmath

well try to use this substitution:
2x-1=u^2, try to defferentiate and substitute back what u get for dx,
you also get for x=(u^2 + 1)/2, from 2x-1=u^2
the rest is pretty simple after u substitute!
Can you go from here?

8. Jan 28, 2008

rocomath

Gets easier as you use it on a daily basis.

First, I would break up the numerator.

$$\int\frac{x^2}{\sqrt{2x-1}}dx-\int\frac{dx}{\sqrt{2x-1}}$$

9. Jan 28, 2008

sutupidmath

It might work this way also, but by immediately taking the substitution that i suggested he will get to the result pretty fast.

10. Jan 28, 2008

anon413

Ok ill try stupid maths method I would get the integral of (((u^2+1)/2)^2-1)/(u) what would my du be

Last edited: Jan 28, 2008
11. Jan 28, 2008

anon413

I guess I will attempt this on my own thats for the help.

12. Jan 28, 2008

sutupidmath

You do not need to know what the du will be, you need just to plug in the value of the dx that you get after differentiating 2x-1=u^2, so it obviously will be dx=udu, and when you plug this in the u here and that one that you will get on the denominator will cancel out so you are left with somehting like this:
$$\int\frac{((\frac{u^{2}+1}{2})^{2}-1)udu}{u}$$, now you can go from here right?

13. Jan 28, 2008

sutupidmath

By the way it is not stupid math, but instead sutupidmath! NOt that i mind it, but it feels good to be correct! NO hard feelings, ok?

14. Jan 28, 2008

anon413

thx stupidmath. I knew I got the right udu for dx.