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∫[(x + 1)/(x*(1 + x*e^x)²)]dx

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\(\huge \int \frac{x+1}{x(1+xe^x)^2}dx=..?\)
partial fractions? or x= log y substitution or how ??
Partial fractions.

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Other answers:

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

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