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## Homework Statement

Find the integral from 3

^{1/2}to 3 of 1/(x) ((x

^{2}+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(3

^{1/2}/3). My answer doesnt 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.