Integrating sqrt(x2+9) - Help Appreciated

[geffman1]

Homework Statement

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 can't see one that looks similar.

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

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

 

[geffman1]

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

 

[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.

 

[HallsofIvy]

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