Integrating sqrt(9x^2-1) Using an Integration Table - How-To Guide

[heighme]

using integration table evaluate the following integral sqrt(9x^2-1)

I just need to know how to start this off, i tried u substitution:

u=9x^2-1 du=18xdx integral:u^(1/2)du/18x. but I don't know how to get rid of the x,

So then from there i tried to use from the integration table integral:udv = uv-(integral vdu)
u=u^1/2 dv=1/18x du=u^(3/2)/(3/2) v=
I didn't know how to go about that

 

[jbunniii]

using integration table evaluate the following integral sqrt(9x^2-1)

I just need to know how to start this off, i tried u substitution:

u=9x^2-1 du=18xdx integral:u^(1/2)du/18x. but I don't know how to get rid of the x,

So then from there i tried to use from the integration table integral:udv = uv-(integral vdu)
u=u^1/2 dv=1/18x du=u^(3/2)/(3/2) v=
I didn't know how to go about that

Try a trig substitution.

 

[Mark44]

Since you explicitly said "using integration table," a trig substitution is probably not the way to go. I'm assuming your integration table has the following integral in it:
$$\int \sqrt{x^2 - a^2} dx$$

Factor 9 out of the two terms in the radical to get 9(x^2 - 1/9).
Bring a factor of 3 out of the radical, and outside the integral.