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hartnn

  • 2 years ago

∫[(x + 1)/(x*(1 + x*e^x)²)]dx

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

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

  3. abb0t
    • 2 years ago
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    Partial fractions.

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

  5. hartnn
    • 2 years ago
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    *polynomial expression

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

  7. hartnn
    • 2 years ago
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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 ...

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

  9. hartnn
    • 2 years ago
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    yeah, what here ?

  10. abb0t
    • 2 years ago
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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

  11. abb0t
    • 2 years ago
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    But it looks like partial should work.

  12. hartnn
    • 2 years ago
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    the answer suggested me partial, but how is the question....

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

  14. hartnn
    • 2 years ago
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    not justified, nor will give complete answer...

  15. abb0t
    • 2 years ago
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    hwat?! :P

  16. LogicalApple
    • 2 years ago
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    Right but what are the steps to derive this?

  17. abb0t
    • 2 years ago
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    ~M*A*G*I*C~

  18. hartnn
    • 2 years ago
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    got it :)

  19. hartnn
    • 2 years ago
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    put 1+xe^x = t

  20. hartnn
    • 2 years ago
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    then partial fractions...

  21. abb0t
    • 2 years ago
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    nicely done, mate :)

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

  23. LogicalApple
    • 2 years ago
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    It's not magic anymore .. :(

  24. mathmate
    • 2 years ago
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    :)

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