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Need help with integration

  1. Nov 13, 2005 #1
    I am trying to integrate sqrt(1+4*x^2)
    I have been trying to rewrite this into sqrt(-4x+(2x + 1)^2) and putting u=2x+1 and substituting but I don't think that makes this any easier. Could someone please give me a hint.
     
  2. jcsd
  3. Nov 13, 2005 #2

    The answer is Partial Integration...Give it a try and let me know

    marlon

    edit hint : do the partial integration right a way with the sqrt(1+4x^2)dx. After this you will need to apply the (+1 -1) trick in the integrand's numerator. If you want you can first do the substitution u=2x to get rid of the 4, but it is not compulsory...
     
    Last edited: Nov 13, 2005
  4. Nov 13, 2005 #3
    After some hard work and a lot of eraser I got the right answer. Thank you marlon.
     
  5. Nov 13, 2005 #4
    Also:

    [tex]\int\sqrt{1+\left(2x\right)^2}\,dx=\frac{1}{2}\int\cosh^2{x}\,dx[/tex]

    Then use the identity for the double angle to simplify that integral.
     
  6. Nov 13, 2005 #5

    benorin

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    Homework Helper

    Try [tex] x=\frac{1}{2}\tan \theta \Rightarrow \sqrt{1+4x^2}=\sec\theta[/tex].
     
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