hartnn
  • hartnn
∫[(x + 1)/(x*(1 + x*e^x)²)]dx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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hartnn
  • hartnn
\(\huge \int \frac{x+1}{x(1+xe^x)^2}dx=..?\)
hartnn
  • hartnn
partial fractions? or x= log y substitution or how ??
abb0t
  • abb0t
Partial fractions.

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More answers

hartnn
  • hartnn
for partial fractions, there should be linear expression, 1+xe^x is not linear....
hartnn
  • hartnn
*polynomial expression
abb0t
  • abb0t
But you do have a function squared. wHICH You can expand to get a ^2x
hartnn
  • hartnn
what would i take in numerator ?? if it were (x+1)^2, i would have taken A/(x+1) +B/(x+1)^2 ...
abb0t
  • abb0t
Yeah, or Ax+B for numerator if you expand it.
hartnn
  • hartnn
yeah, what here ?
abb0t
  • abb0t
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
abb0t
  • abb0t
But it looks like partial should work.
hartnn
  • hartnn
the answer suggested me partial, but how is the question....
abb0t
  • abb0t
\[\frac{ A}{ x } + \frac{ Bx+C }{ (1+xe^x) }+...\]
hartnn
  • hartnn
not justified, nor will give complete answer...
abb0t
  • abb0t
hwat?! :P
hartnn
  • hartnn
http://www.wolframalpha.com/input/?i=integral+%5B%28x+%2B+1%29%2F%28x*%281+%2B+x*e%5Ex%29%C2%B2%29%5Ddx
anonymous
  • anonymous
Right but what are the steps to derive this?
abb0t
  • abb0t
~M*A*G*I*C~
hartnn
  • hartnn
got it :)
hartnn
  • hartnn
put 1+xe^x = t
hartnn
  • hartnn
then partial fractions...
abb0t
  • abb0t
nicely done, mate :)
hartnn
  • hartnn
\(\huge \int \frac{e^x(x+1)}{x.e^x(1+xe^x)^2}dx=\int \frac{dy}{y^2(y-1)}\)
anonymous
  • anonymous
It's not magic anymore .. :(
mathmate
  • mathmate
:)

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