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Trig substitution integral

  • Thread starter montana111
  • Start date
  • #1
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Homework Statement


evaluate the integral using the indicated trig substitution. sketch the corresponding right triangle.

integral of(1/(x^2 sqrt(x^2 - 9))


Homework Equations



integral of(1/(x^2 sqrt(x^2 - 9))

The Attempt at a Solution


at first glance this seemed really easy, and i tried doing it without the given trig substitution of 3sec(theta), but i just got confused. i made the triangle with 3 on the hypotenuse and x on the leg opposite theta. then i said x = 3sin(theta) (because i have a value for the hypotenuse and the opposite) and from there i have no idea what to do. Also, im discouraged because the book tells you to use 3sec(theta) which is driving me insane because i have no idea why i would use sec at all. thanks for you help.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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The hint is infact very useful.

you have:

[tex]\int\frac{1}{x^2\sqrt{x^2-9}}dx[/tex]

using the substitution x = 3sec[tex]\theta[/tex]
you will get a simple integral.

substitute this into the integral. BUT... you have to first find dx/d[tex]\theta[/tex] in order to substitute something for dx (in terms of d[tex]\theta[/tex])

so after the substitution, what do you get?
(You might like to remember also the identity (sec[tex]\theta[/tex])^2-1=tan([tex]\theta[/tex])^2)
:wink:
 
  • #3
33,639
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montana111 said:
i made the triangle with 3 on the hypotenuse and x on the leg opposite theta.
Since the radical contains x2 - 9, you want x on the hypotenuse and 3 on one leg, and sqrt(x2 - 9) on the other leg.
 

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