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How to solve this integral

  1. Feb 14, 2014 #1
    I cannot find a substitution that work for this integral

    ∫dx/2√x+2x

    what should I do?
     
  2. jcsd
  3. Feb 14, 2014 #2

    statdad

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    What is [itex] \left(\sqrt{x}\right)^2[/itex]?
     
  4. Feb 14, 2014 #3
    it is∫dx/2sqrt(x)+2x
     
  5. Feb 14, 2014 #4

    PhysicoRaj

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    See what you can do to bring a function and it's derivative.. you have √x in the denominator so you should think in terms of derivative of that.
     
  6. Feb 14, 2014 #5

    statdad

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    If the integral is
    [tex]
    \int \frac{1}{2 \sqrt{x} + 2x} \, dx
    [/tex]

    thinking about the derivative of [itex] \sqrt{x} [/itex] alone will not help.
     
  7. Feb 14, 2014 #6
    yes, this is the integral
     
  8. Feb 14, 2014 #7

    PhysicoRaj

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    If he tries to bring the derivative of √x so that it is in product with the original function √x, he can substitute easily. That's what I meant.
     
  9. Feb 14, 2014 #8

    PhysicoRaj

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    Convert the addition form in the denominator into product form so that the function and it's derivative are seen clearly in multiplied form.
     
  10. Feb 14, 2014 #9

    vanhees71

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    Then think about the obvious substitution, aiming to get rid of the square root :-).
     
  11. Feb 14, 2014 #10
    thank you
     
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