hartnn
∫[(x + 1)/(x*(1 + x*e^x)²)]dx



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

hartnn
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partial fractions? or x= log y substitution or how ??

abb0t
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Partial fractions.

hartnn
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for partial fractions, there should be linear expression,
1+xe^x is not linear....

hartnn
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*polynomial expression

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

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 ...

abb0t
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Yeah, or Ax+B for numerator if you expand it.

hartnn
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yeah, what here ?

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

abb0t
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But it looks like partial should work.

hartnn
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the answer suggested me partial, but how is the question....

abb0t
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\[\frac{ A}{ x } + \frac{ Bx+C }{ (1+xe^x) }+...\]

hartnn
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not justified, nor will give complete answer...

abb0t
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hwat?! :P


LogicalApple
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Right but what are the steps to derive this?

abb0t
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~M*A*G*I*C~

hartnn
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got it :)

hartnn
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put 1+xe^x = t

hartnn
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then partial fractions...

abb0t
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nicely done, mate :)

hartnn
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\(\huge \int \frac{e^x(x+1)}{x.e^x(1+xe^x)^2}dx=\int \frac{dy}{y^2(y1)}\)

LogicalApple
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It's not magic anymore .. :(

mathmate
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:)