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welshfella

  • one year ago

Integrate 1 / (x^10 + x) 1

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  1. welshfella
    • one year ago
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    I'm not sure about the best way to approach this one.

  2. welshfella
    • one year ago
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    partial fractions does n't help

  3. ganeshie8
    • one year ago
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    multiply top and bottom by \(x^{-10}\) : \[\int \dfrac{x^{-10}}{1+x^{-9}}\,dx\]

  4. welshfella
    • one year ago
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    ah!!!

  5. ganeshie8
    • one year ago
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    next step is obvious sub \(u = 1+x^{-9}\)

  6. welshfella
    • one year ago
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    so its -1/9 ln (1 + x^-9)?

  7. ganeshie8
    • one year ago
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    looks good !

  8. welshfella
    • one year ago
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    thank you

  9. ganeshie8
    • one year ago
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    np

  10. welshfella
    • one year ago
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    integration is an art...

  11. ganeshie8
    • one year ago
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    definitely almost every integration problem requires guessing and makes mathematicians feel humble of the fact that we can't integrate everything into an elementary function ;)

  12. welshfella
    • one year ago
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    too true

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