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Integration help

  1. Jun 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi,

    I am not sure if you can use a u-substitution on this integral, [tex] \int \frac{1}{\sqrt{9x^{2}+4}} dx [/tex]?

    [tex] \sqrt{9x^{2}+4} [/tex]

    Can I?

    I have tried it, but get an even more complicated integral from what I started with.
     
  2. jcsd
  3. Jun 13, 2010 #2
    You can refer to the standard integrals in the PF library to get the solution directly.
     
  4. Jun 13, 2010 #3

    Thank you, but the table does not show me a method, and I would really like to know how to go about this.


    I am right in saying we can use a substitution?
     
  5. Jun 13, 2010 #4

    Gib Z

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    Homework Helper

    You can use a substitution, but not the one you used. Have you learned the theory and method of trigonometric substitutions?
     
  6. Jun 14, 2010 #5
    Could you think of using the trigonometric relation [itex] sin^2x+cos^2x=1[/itex] to simplify your integral.
     
  7. Jun 14, 2010 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If that isn't a sufficient hint note that dividing both sides of [itex]sin^2 x+ cos^2 x= 1[/itex] by [itex]cos^2 x[/itex] gives [itex]tan^2 x+ 1= sec^2 x[/itex] and that
    [tex]\sqrt{9x^2+ 4}= \sqrt{\frac{1}{4}\left(\frac{9x^2}{4}+ 1\right)}= \frac{1}{2}\sqrt{\left(\frac{3x}{2}\right)^2+ 1}[/tex]
     
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