Tricky Integral?

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  • #1
iatnogpitw
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Tricky Integral??

Homework Statement



So the problem is to integrate this:

{(x^2) / sqrt[(x^2) - 9] } dx

I cannot, for the life of me, solve this problem, and I know it's not that hard. I have tried using trig substitutions x = 3 cos(theta) and x = 3 sec(theta) but for some reason, maybe a math error, it doesn't work out. Can someone compute this for me and give steps?
 

Answers and Replies

  • #2
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Your trig substitution is set up wrong. Draw a right triangle with x as the hypotenuse and 3 as the base. The altitude will be sqrt(x^2 - 9). The substitution is sec(theta) = x/3. Using this substitution should get you to [itex]27\int sec^3(\theta) d\theta[/itex]. That one requires integration by parts once or twice, if I recall correctly.
 

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