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Math Help - Quick Integration problem

  1. #1
    is up to his old tricks again! Jhevon's Avatar
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    Quick Integration problem

    This is not a very difficult problem, it's just that I did calc 2 a while back and I'm really rusty. Here goes:

    Int(1/(1+x+x^2))dx

    The problem I'm having is not with the integration per say, but everything leading up to it. I'm pretty sure you have to manipulate it so that it is in the form 1/(1+u^2) and then use arctan, but I can't seem to do that. So whoever decides to answer this question, can you please show all the steps. Thanks
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  2. #2
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    Quote Originally Posted by Jhevon View Post
    This is not a very difficult problem, it's just that I did calc 2 a while back and I'm really rusty. Here goes:

    Int(1/(1+x+x^2))dx

    The problem I'm having is not with the integration per say, but everything leading up to it. I'm pretty sure you have to manipulate it so that it is in the form 1/(1+u^2) and then use arctan, but I can't seem to do that. So whoever decides to answer this question, can you please show all the steps. Thanks
    You are correct.
    You need to use a classic trick, "completing the square".
    Attached Thumbnails Attached Thumbnails Quick Integration problem-picture1.gif  
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    thanks

    Thanks a lot, got it.
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  4. #4
    Math Engineering Student
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    This integral produces an inverse trig. function



    Applyin' this, yields:

    Last edited by ThePerfectHacker; March 10th 2007 at 02:58 PM.
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