What Integration Technique to Use for \int\sqrt{x^2-1}dx

[Abraham]

Homework Statement

Solve:

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

Homework Equations

This is where I need help. What integration technique do I use? u-substitution? Integration by parts? None seem to work. As an added note, I've been trying to teach myself some calculus II work over the summer, so I just need a pointer in the right direction. Thank you

The Attempt at a Solution

I attempted to use u-substitution. I don't think this is the right method. Does anyone know the correct method? It got pretty messy, but I didn't get the right answer:

$$\int$$$$\sqrt{x^{2}+1}$$dx


u = $$x^{2}$$+1
du = 2x
x = $$\sqrt{u-1}$$



= $$\frac{1}{2}$$ $$\int$$($$\sqrt{u}$$)($$\sqrt{u-1}$$) du


= ? Is this the correct start?

 

[Feldoh]

Try tan(u) = x as the substitution.

 

[WiFO215]

Let I = $$\int\sqrt{x^2-1}$$dx

Try integrating by parts.

I = $$x\sqrt{x^2-1}dx$$ - $$\int x\x^{2} / \sqrt{x^2-1}dx$$

See if you can carry on from here.

 

[physicsnoob93]

I KNOW this will work. Sub x as sec(u). Go on from there.

 

[WiFO215]

I KNOW this will work. Sub x as sec(u). Go on from there.

What are you implying sir? I'm sure all of us here know how to complete the problem easily. I didn't want to solve the problem for him. Therefore I gave him a hint so that he could carry on from there.

 

[physicsnoob93]

What are you implying sir? I'm sure all of us here know how to complete the problem easily. I didn't want to solve the problem for him. Therefore I gave him a hint so that he could carry on from there.

Sorry, I didn't mean to offend anyone. And I didn't mean your hint was worthless.

 

[WiFO215]

Sorry, I didn't mean to offend anyone.

It's cool.

 

[jeff1evesque]

Random fact, but you can always check your integration calculation online (if you don't have a graphing calculator):
http://integrals.wolfram.com/index.jsp