## hartnn 2 years ago ∫[(x + 1)/(x*(1 + x*e^x)²)]dx

1. hartnn

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

2. hartnn

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

3. abb0t

Partial fractions.

4. hartnn

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

5. hartnn

*polynomial expression

6. abb0t

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

7. hartnn

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

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

9. hartnn

yeah, what here ?

10. 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

11. abb0t

But it looks like partial should work.

12. hartnn

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

13. abb0t

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

14. hartnn

not justified, nor will give complete answer...

15. abb0t

hwat?! :P

16. hartnn
17. LogicalApple

Right but what are the steps to derive this?

18. abb0t

~M*A*G*I*C~

19. hartnn

got it :)

20. hartnn

put 1+xe^x = t

21. hartnn

then partial fractions...

22. abb0t

nicely done, mate :)

23. hartnn

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

24. LogicalApple

It's not magic anymore .. :(

25. mathmate

:)