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hartnn

∫[(x + 1)/(x*(1 + x*e^x)²)]dx

  • one year ago
  • one year ago

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  1. hartnn
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    \(\huge \int \frac{x+1}{x(1+xe^x)^2}dx=..?\)

    • one year ago
  2. hartnn
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    partial fractions? or x= log y substitution or how ??

    • one year ago
  3. abb0t
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    Partial fractions.

    • one year ago
  4. hartnn
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    for partial fractions, there should be linear expression, 1+xe^x is not linear....

    • one year ago
  5. hartnn
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    *polynomial expression

    • one year ago
  6. abb0t
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    But you do have a function squared. wHICH You can expand to get a ^2x

    • one year ago
  7. hartnn
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    what would i take in numerator ?? if it were (x+1)^2, i would have taken A/(x+1) +B/(x+1)^2 ...

    • one year ago
  8. abb0t
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    Yeah, or Ax+B for numerator if you expand it.

    • one year ago
  9. hartnn
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    yeah, what here ?

    • one year ago
  10. abb0t
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    I think you can use Ax+B w/o expanding. haha. I'm just making guesses now. I don't have a pen within a 12 inch radius Lol

    • one year ago
  11. abb0t
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    But it looks like partial should work.

    • one year ago
  12. hartnn
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    the answer suggested me partial, but how is the question....

    • one year ago
  13. abb0t
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    \[\frac{ A}{ x } + \frac{ Bx+C }{ (1+xe^x) }+...\]

    • one year ago
  14. hartnn
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    not justified, nor will give complete answer...

    • one year ago
  15. abb0t
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    hwat?! :P

    • one year ago
  16. hartnn
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    http://www.wolframalpha.com/input/?i=integral+%5B%28x+%2B+1%29%2F%28x*%281+%2B+x*e%5Ex%29%C2%B2%29%5Ddx

    • one year ago
  17. LogicalApple
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    Right but what are the steps to derive this?

    • one year ago
  18. abb0t
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    ~M*A*G*I*C~

    • one year ago
  19. hartnn
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    got it :)

    • one year ago
  20. hartnn
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    put 1+xe^x = t

    • one year ago
  21. hartnn
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    then partial fractions...

    • one year ago
  22. abb0t
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    nicely done, mate :)

    • one year ago
  23. hartnn
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    \(\huge \int \frac{e^x(x+1)}{x.e^x(1+xe^x)^2}dx=\int \frac{dy}{y^2(y-1)}\)

    • one year ago
  24. LogicalApple
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    It's not magic anymore .. :(

    • one year ago
  25. mathmate
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    :)

    • one year ago
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