Simple Integration using U Substitution

[anon413]

Homework Statement

Find the indefinite integral.
The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx

Homework Equations

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.

 

[rocomath]

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

Yes?

 

[anon413]

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

 

[anon413]

How did you type that exactly.

 

[rocomath]

How did you type that exactly.

LaTeX https://www.physicsforums.com/showthread.php?t=8997

Check my thread again, I editted it. Is it correct now?

 

[anon413]

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

 

[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?

 

[rocomath]

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

Gets easier as you use it on a daily basis.

First, I would break up the numerator.

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

 

[sutupidmath]

Gets easier as you use it on a daily basis.

First, I would break up the numerator.

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

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

 

[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

 

[anon413]

I guess I will attempt this on my own that's for the help.

 

[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?

 

[sutupidmath]

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

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?

 

[anon413]

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