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Evaluating improper intergral with trig function

  1. Sep 6, 2015 #1
    1. The problem statement, all variables and given/known data

    Okay so the problem is asking simply for a proof for convergence /divergence of the following indefinite integral:

    ∫(x*sin2(x))/(x3-1) over [2,∞)

    2. Relevant equations

    I know I can use substitution method
    3. The attempt at a solution

    Okay so I know if i factorize the bottom part of the integral I get:

    ∫(x*sin2(x))/(x-1)(x-1)(x2+x+1).

    Now obviously I am not sure if this a very elemetary problem or indeed quite challenging. I have tried substituion making u = (x3-1) but than didn't really work... Not sure what else I should try
     
  2. jcsd
  3. Sep 6, 2015 #2
    I dont think that the problem wants you to solve the improper integral. Rather, it wants you to perform some test for convergence / divergence.
     
  4. Sep 6, 2015 #3

    That's what I thought, as the computation of the improper integral would probably be too challenging... Should I use the limit test? In other words compare the overall function to the convergence/divergence of 1/x3 as it approaches 2
     
    Last edited: Sep 6, 2015
  5. Sep 6, 2015 #4

    Ray Vickson

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    Homework Helper

    You don't need to worry about the lower limit x = 2, because nothing bad happens to the integrand ##f(x) = x \sin^2(x)/(x^3-1)## as ##x \to 2##. However, you do need to worry about the upper limit as ##x \to \infty##. Your textbook and/or course notes must have some relevant tests to use; try out some of them, then come back here if you still have some questions and issues.
     
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