# How to Integrate

1. Feb 18, 2009

### 930R93

Problem:
$$\int\sqrt{x^{2}+2}/x$$

Attempt:
Let x= $$\sqrt{2}$$ sin$$\vartheta$$
dx= $$\sqrt{2}$$ cos$$\vartheta$$ d$$\vartheta$$

from this I got

$$\int\sqrt{2}sin\theta\sqrt{2}cos\theta/\sqrt{2}cos\theta$$

I think inverse substitution was not the right way to solve this problem...
any help would be greatly appreciated! Thanks!

2. Feb 18, 2009

### Tom Mattson

Staff Emeritus
That's fine.

That's not fine. If $x=\sqrt{2}\sin(\theta)$ then shouldn't there be a sine function in the denominator? And why is there a sine function in the numerator?

3. Feb 18, 2009

### 930R93

Yikes! I saw (2-x^2)^(1/2) in the numerator and used a trig identity to simplify the top...
so after you pointed this out i corrected the mistake and am left with nothing (from my point of view) i can simplify... i have root(2)*root(sin^2(O) +1)*root(2)*cos(O)dO over (root(2)*sinO)

umm...

4. Feb 19, 2009

### Tom Mattson

Staff Emeritus
That's not what you had in the original problem. What's going on here?

5. Feb 19, 2009

### aostraff

If the posted question is the one you want to solve, think about the the trig identity relating tan and sec.

6. Feb 19, 2009

### 930R93

Hey thanks! Im not sure why I didn't see this. I got it! thanks again!

7. Feb 19, 2009

### 930R93

Sorry, it was a mistake on my end; I didn't give a very clear question. I used sine and cosine instead of tan and sec. whoops! it got it though but thanks for trying to help me, ill have to get better at asking if i want any help lol. :tongue:

-930R93