Calc II integration by trig sub

  • Thread starter Rock32
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  • #1
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Homework Statement



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?

The books answer is: 1/6ln((3-2*21/2)(7+4*31/2

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.
 

Answers and Replies

  • #2
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Is this your integral?
[tex]\int_{\sqrt{3}}^3 \frac{\sqrt{x^2 + 9}}{x}dx[/tex]
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.
 

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