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Computing antiderivatives (integration)

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data
    integrate 4e^(2x)^(1/2) - 1/7e^(-pix)
    using a guess and check method (haven't learned many rules of integration)


    2. Relevant equations



    3. The attempt at a solution
    i'm not really sure how to do this integral... i tried
    4/(2x)^(1/2)[e^(2x)^(1/2)] using a table of antiderivatives for the first part
    but when i differentiated it, it did not give me the original function
    i haven't tried the second bit yet.
     
  2. jcsd
  3. Jan 18, 2012 #2
    For the second term, do you know how to differentiate exponential functions?

    Can you answer these questions, differentiate with respect to x:

    e^x
    18e^x
    4e^2x
    e^(x^2)
    e^(x^(1/3))
    e^(8x^(-2/3))

    For the first term you need to use a substitution, try substituting u=x^1/2
     
  4. Jan 18, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If you have [itex]\int f'(x)e^{f(x)}dx[/itex] you could make the substitution [tex]u= f(x)[/tex] so that [tex]du= f'(x)dx[/tex] and the integral becomes [tex]\int e^u du= e^u+ C= e^{f(x)}+ C[/tex]

    HOWEVER, if that f'(x) is not in the integral originally (and is not a constant), you cannot put it in! Here, I don't believe that [tex]\int e^{(4x)^{1/2}}dx[/tex] can be integrated in terms of elementary functions.
     
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