intergration (basic)

[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:rolleyes:

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

[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).