SOLUTION: integrate {{{matrix(2,1,"", (e^(x^2+2x))/((x+1)^2)))}}} Thanks!

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Question 1010978: integrate
Thanks!
Found 4 solutions by Fombitz, fractalier, Edwin McCravy, ikleyn:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There is not a closed form solution to this problem if that's what you're looking for.
If that's not what you want, please repost and clarify.

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
I do not believe I can give you a closed-form solution to this integral...if you give me limits, we can do it numerically...

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Cannot be integrated in closed form by any methods taught in
college mathematics.
It can be expanded in a Taylor (MacLaurin) series

and integrated term by term:




Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
integrate
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1.  Multiply the numerator by  e  and divide the function by  e.  The integrand does not change,  it remains the same:

= matrix%282%2C1%2C%22%22%2C%281%2Fe%29%29. = matrix%282%2C1%2C%22%22%2C%281%2Fe%29%29.


2.  Replace the variable  y = x+1.  You will get

matrix%282%2C1%2C%22%22%2C%281%2Fe%29%29. = matrix%282%2C1%2C%22%22%2C%281%2Fe%29%29.matrix%282%2C1%2C%22%22%2C%0D%0A%0D%0A%28e%5E%28y%5E2%29%2Ady%29%2F%28y%5E2%29%29%29


3.  Take the integral by parts:   u = matrix%282%2C1%2C%22%22%2Ce%5E%28y%5E2%29%29,   v*dy = %28dy%29%2F%28y%5E2%29,   v = -1%2Fy.

Do not forget this factor  1%2Fe.

4.  In this way you will reduce the problem to the integral of the function   matrix%282%2C1%2C%22%22%2Ce%5E%28y%5E2%29%29.

This integral is not an elementary function,  and it is entirely out of the school Calculus.  It is entirely out of the university Calculus,  even.