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Math Help - Integration

  1. #1
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    Exclamation Integration

    Hi

    How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

    PS I got that after using the t method trying to integrate 1/((cosx)^2+1)
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    Hi

    How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

    PS I got that after using the t method trying to integrate 1/((cosx)^2+1)
    \int{\frac{t^2}{t^4 + 1}\,dt}

    http://www.wolframalpha.com/input/?i=integral[%28x^2%29%2F%28x^4+%2B+1%29]

    Click "Show Steps".
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    Ummm the computer uses partial fractions but I dont think i am capable of figuring such long denominators out during the exam...is there another way?
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    Quote Originally Posted by xwrathbringerx View Post
    Ummm the computer uses partial fractions but I dont think i am capable of figuring such long denominators out during the exam...is there another way?
    I'd say there isn't - the computer probably wouldn't resort to partial fractions unless absolutely necessary.
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  5. #5
    Ted
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    Quote Originally Posted by xwrathbringerx View Post
    Hi

    How exactly do I integrate t^2/(t^4+1) without using partial fractions (cause that looks soooo complicated)?

    PS I got that after using the t method trying to integrate 1/((cosx)^2+1)
    \int \frac{t^2}{t^4+1} dt = \int \left( \sum_{n=0}^{\infty} (-1)^n t^{4n+2} \right) dt.
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