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Math Help - How to find this integral

  1. #1
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    How to find this integral

    Yeah, so I can't figure out how to find the integral with respect to x of the following

    cos(x) / (1 + x).


    how would I do this?

    thanks for any help
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  2. #2
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    Quote Originally Posted by snoboarder2k6 View Post
    Yeah, so I can't figure out how to find the integral with respect to x of the following

    cos(x) / (1 + x).


    how would I do this?

    thanks for any help
    Why? The reason I ask is this:
    Attached Thumbnails Attached Thumbnails How to find this integral-msp.gif  
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  3. #3
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    yeah, I did try the integration calculator. I just have no idea what those symbols mean. What's the w/ the Si(...) Ci(...) etc?
    That and I want to know how to do it w/o the help of a computer so I can handle it on a test if i need to.

    thanks
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  4. #4
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    Quote Originally Posted by snoboarder2k6 View Post
    yeah, I did try the integration calculator. I just have no idea what those symbols mean. What's the w/ the Si(...) Ci(...) etc?
    That and I want to know how to do it w/o the help of a computer so I can handle it on a test if i need to.

    thanks
    What it means old son is that there's no answer in terms of a finite number of elementary functions.

    If you haven't met the sine-integral Si(x) and cos-integral Ci(x) functions then I would be mighty surprised to see them required on your test ....... Where has the question come from?

    Are you sure you not asked to get definite integrals, say form 0 to oo?
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  5. #5
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    this was part of a larger linear equation, so I'm gonna assume I screwed up somewhere else and that I shouldn't even have to do this.

    Thanks for you're help though
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  6. #6
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    Quote Originally Posted by snoboarder2k6 View Post
    Yeah, so I can't figure out how to find the integral with respect to x of the following

    cos(x) / (1 + x).


    how would I do this?

    thanks for any help
    \int \frac{\cos (x)}{x+1} dx = \int \frac{\cos [(x+1)-1]}{(x+1)}\left( x+1 \right) ' ~ dx = \int \frac{\cos (x+1)\cos 1 + \sin (x+1)\sin 1}{(x+1)} \left( x+1 \right) ' ~ dx = \mbox{Ci}(x+1)\cos 1 + \mbox{Si}(x+1)\sin 1 + k
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