# Intergration (basic)

1. May 14, 2009

### geffman1

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

hey guys i was wondering if anyone could show my how to intergrate sqrt(x2+9). any help would be greatfully appreciated. the sqaure root is over everything

P.s i have looked at table of intergral but cant see one that looks similar.

2. Relevant equations

3. The attempt at a solution

2. May 14, 2009

### gabbagabbahey

Use integration by parts with $u=\sqrt{x^2+9}$ and $dv=dx$...

3. May 14, 2009

### geffman1

thanks but i have never used any of those methods before?

4. May 14, 2009

### Cyosis

You haven't been taught integration by parts yet? Do you know substitutions, if so try $x=3 \sinh u$. If both these methods are alien to you they probably expect you to compare it to a standard integral somewhere listed in the back or front of your calculus book.

5. May 14, 2009

### HallsofIvy

Staff Emeritus
Yet another way is to let $x= 3tan(\theta)$. Then $dx= 3sec^2(\theta)$ and $\sqrt{x^2+ 9}= \sqrt{9tan^2(\theta)+ 9}= 3\sqrt{tan^2(\theta)+ 1}= 3sec(\theta)$.