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Math Help - Comparison Theorem Help

  1. #1
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    Comparison Theorem Help

    I have a calculus problem that I just can't seem to figure out...

    We are asked to prove that the integral ∫((arctanx)/e^x) from 0 to ∞ converges by using the comparison theorem. I understand the comparison theorem, but I don't understand what integral to pick to compare it to... do I pick at random, or is there a method to solving it?

    Thanks in advance
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  2. #2
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    Quote Originally Posted by mxrider530 View Post
    We are asked to prove that the integral ∫((arctanx)/e^x) from 0 to ∞ converges by using the comparison theorem.
    You know that \int_0^\infty  {\frac{{dx}}{{e^x }}}  = 1.

    Also take notice that \arctan (x) < \frac{\pi }{2}.
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