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Homework Help: Integrals of exponentials

  1. Oct 23, 2008 #1
    1. The problem statement, all variables and given/known data
    Integrate: x.e[tex]^{2x^{2}}[/tex]


    2. Relevant equations

    None.

    3. The attempt at a solution

    I first thought that the coefficient 2 in "2x" would become the denominator:

    [tex]\frac{x.e^{2x^{2}}}{2}[/tex]

    and then integrating the x would mean x^2 and division by another two making the answer:

    [tex]\frac{x^{2}.e^{2x^{2}}}{4}[/tex]

    But the answer listed in the book doesn't have an x^2, it's only
    [tex]\frac{e^{2x^{2}}}{4}[/tex]

    What did I do wrong?
     
  2. jcsd
  3. Oct 23, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    You didn't do anything right! You know, I hope, that the derivative of product is NOT just the product of the derivatives: (fg)'= f'g+ fg', not f'g'. So you can't expect that the integral of a product will just be the product of the integrals: the integral of fg is not just the integral of f times the integral of g.

    Here, you need to make a substitution: if u= x2, what is du/dx? What is du in terms of dx?
     
  4. Oct 23, 2008 #3
    It would be 2x.dx of course.

    So I guess the substitution you want me to make is u = 2x^{2} ? Therefore du/dx= 4x.dx
    And then it would be [tex]du/4.e^{u}[/tex]

    But then I don't see how that becomes the correct answer.
     
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