# Homework Help: Calc II integration by trig sub

1. Sep 11, 2009

### Rock32

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

Find the integral from 31/2 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 isnt even close to sec(arctan(3/3)-sec(arctan(31/2/3). My answer doesnt match the books. Maybe its a domain problem?

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.

2. Sep 11, 2009

### Staff: Mentor

$$\int_{\sqrt{3}}^3 \frac{\sqrt{x^2 + 9}}{x}dx$$
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.