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Calculate integral sin(x)/x^0.1dx from pi to infinity

  1. Sep 23, 2015 #1
    1. The problem statement, all variables and given/known data
    So I have a problem with the integral

    ∫ sin(x)/x^0.1dx from pi to infinity

    My teacher said this wouldn't require any maths beyond calc 3, but for some reason I cannot come up with a solution.
    2. Relevant equations


    3. The attempt at a solution
    I have attempted a maclaurin series to replace the sin(x) term but the series does not converge so that doesnt work.
    I tried integration by parts which just keeps reppeating the sin and cos terms with x^.1 in the denominator

    I attempted substitution but that clearly doesn't work.
    I even attempted contour integration but I dont think that could be the solution as we have not done that yet and that is not at the calc 3 level.

    Is there anything I'm mising!?
     
  2. jcsd
  3. Sep 23, 2015 #2

    andrewkirk

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    If it's any consolation, Wolfram Alpha gives the indefinite integral of this function as a complicated function involving imaginary numbers and the Incomplete Gamma Function, neither of which would typically be covered in introductory calculus courses.
     
  4. Sep 23, 2015 #3
    That's literally the first thing I did was to plug it into wolfram alpha! THats how I knew this wasn't going to be a picnic. The professor says that there is something in calc 3 I would've learned that makes solving this possible but I have no idea what (the professor is Russian btw) and he refuses to give out more info than that. The only thing I can maybe see is that sin(x) can be replaced by 1 and we can find the limit like that and see that it converges but that doesnt help me solve this problem
     
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