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Math Help - Midterm coming up! one question

  1. #1
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    Midterm coming up! one question

    For study for the review, we recieved a couple questions. However, I got stuck on this. if you can help then itd be real awesome...

    The integral of x / (1 + x^4), from 1 to infinity... find convergance...
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  2. #2
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    Quote Originally Posted by 3deltat View Post
    For study for the review, we recieved a couple questions. However, I got stuck on this. if you can help then itd be real awesome...

    The integral of x / (1 + x^4), from 1 to infinity... find convergance...
    \int \limits_1^{\infty} \frac{x}{x^4+1} dx = \frac{1}{2} \int \limits_1^{\infty} \frac{(x^2)'}{(x^2)^2+1}dx = \frac{1}{2} \int \limits_1^{\infty} \frac{d\mu }{\mu^2 +1} = \frac{\pi}{4}

    Not only did we show it converges we showed what the value is.
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