# Which Integration Technique?

1. Aug 15, 2009

### Abraham

1. The problem statement, all variables and given/known data

Solve:

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

2. Relevant 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

3. 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?

2. Aug 15, 2009

### Feldoh

Try tan(u) = x as the substitution.

3. Aug 15, 2009

### 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.

4. Aug 15, 2009

### physicsnoob93

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

5. Aug 15, 2009

### WiFO215

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.

6. Aug 15, 2009

### physicsnoob93

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

7. Aug 15, 2009

### WiFO215

It's cool.

8. Aug 15, 2009