∫[(x + 1)/(x*(1 + x*e^x)²)]dx

Question

hartnn · Answer

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

hartnn · Answer

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

abb0t · Answer

Partial fractions.

hartnn · Answer

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

hartnn · Answer

*polynomial expression

abb0t · Answer

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

hartnn · Answer

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

abb0t · Answer

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

hartnn · Answer

yeah, what here ?

abb0t · Answer

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 · Answer

But it looks like partial should work.

hartnn · Answer

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

abb0t · Answer

$$\frac{ A}{ x } + \frac{ Bx+C }{ (1+xe^x) }+...$$

hartnn · Answer

not justified, nor will give complete answer...

abb0t · Answer

hwat?! :P

hartnn · Answer

anonymous · Answer

Right but what are the steps to derive this?

abb0t · Answer

~M*A*G*I*C~

hartnn · Answer

got it :)

hartnn · Answer

put 1+xe^x = t

hartnn · Answer

then partial fractions...

abb0t · Answer

nicely done, mate :)

hartnn · Answer

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

anonymous · Answer

It's not magic anymore .. :(

mathmate · Answer

:)