Calc II integration by trig sub

[Rock32]

Homework Statement

Find the integral from 3^1/2 to 3 of 1/(x) ((x² +9))^1/2


I tried to substitute x= 3tanu, and I get down eventually to a solution that is (sec(pi/4) - sec(pi/6))

I realize integrals can have many forms, but the form in the back of my book isn't even close to sec(arctan(3/3)-sec(arctan(3^1/2/3). My answer doesn't match the books. Maybe its a domain problem?

The books answer is: 1/6ln((3-2*2^1/2)(7+4*3^1/2

Sorry, I'm exhausted, and I do not have the energy to type out how I got from the tangent substitution to my final value.

Any help would be great.

 

[Mark44]

Is this your integral?
$$\int_{\sqrt{3}}^3 \frac{\sqrt{x^2 + 9}}{x}dx$$
Your substitution looks to be the correct one, but if you're not getting the same answer as in your text, possibly you made a mistake after doing the substitution. It's also possible, but less probable, that the book's answer is wrong.