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I am trying to get bound for the following integral $$ \int_0^{\infty}\frac{1}{|x|^r}dx, \mbox{for } 1\leq r< \infty $$ In particular, the bound of the form $\frac{constant}{r}$.

Sorry, we can omit the absolute value. And probably consider interval $(a,\infty)$ for some $a$ very close to 0. So, the integral is $$ \int_a^{\infty}\frac{1}{x^r}dx, \mbox{for } 1\leq r< \infty $$

  • 4
    Do you want $\int_a^\infty {1\over |x|^r}\,dx$ for some $a>0$? As it stands, the integral never converges.2012-01-21
  • 0
    I think that the absolute value signs can be omitted, or should we interpret it as a complex integral?2012-01-21
  • 2
    I would assume that you can find the exact value of the integral.2012-01-21

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