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Working problem 3 ways

  • Thread starter shadow5449
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  • #1
I have to work this problem 3 ways, and I've gotten two, but am not sure about the third way.

integral (x/sqrt(x^2-9))dx
the first way I worked by setting u = x^2 - 9
the second way I worked by setting x = 3sec(theta)
but the third way I have no clue, the book gave us a hint: Let x^2 - 9 = (sin(theta))^2

Thanks
 

Answers and Replies

  • #2
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1
Do exactly what you did with x = 3sec(theta), but this time with the identity x^2 - 9 = (sin(theta))^2.

x = sqrt((sin(theta)^2)+9);
dx = sin(theta)cos(theta)(((sin(theta)^2)+9)^-.5) d(theta)

Plug that in (and the x^2 value) and solve; you answer should come up to be sin(theta) + C. Then all you need to do is change back in terms of x.
 
Last edited:

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