Integration help

  • Thread starter tweety1234
  • Start date
  • #1
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Homework Statement



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.
 

Answers and Replies

  • #2
245
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You can refer to the standard integrals in the PF library to get the solution directly.
 
  • #3
112
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You can refer to the standard integrals in the PF library to get the solution directly.


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?
 
  • #4
Gib Z
Homework Helper
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You can use a substitution, but not the one you used. Have you learned the theory and method of trigonometric substitutions?
 
  • #5
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Could you think of using the trigonometric relation [itex] sin^2x+cos^2x=1[/itex] to simplify your integral.
 
  • #6
HallsofIvy
Science Advisor
Homework Helper
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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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