Integral

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Frogger888

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Feb 2, 2006
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I have the integral: Integral (x^(3)*e^(2x))dx/[(2x(^2)+1)^(2)]
What method would I go about solving this. I have tried integration of parts and it does not work since there is not a finite number of derivatives for the polynomials; Hence I tried the tabular method. Next I looked at a possible substitution and could not find anything to use for u except maybe 2x but again I cant get it worked past that because nothing cancels out the x cubed. If anyone can help me by letting me know what method would be the most productive feel free to chime in. :shock:
Thanks
 
Have you tried Partial Fraction Decomposition on the Rational Function part? It won't take you very far, but it appears to get farther than you have gotten.

You should note, up front, that you really won't get very far using ANY methodology that caters to simple functions only, such as those methods you have suggested. For elementary functions and methods, that's just a crazy function.

How are your numerical methods or series methods?
 
Actually I was helping one of my friends solve this equation and realized that wow I have no clue how to solve it so no my curiousity has got the best of me and I want to see how to do it. There is an example in her calculus book but she did not have the solution manual with her. I think if I look at that I will be able to get a good idea of what is going on with that integral.
Thanks

I am not very familiar anymore with the things you suggested without reviewing my old Calculus notes etc...
:)
 
I hardly can wait.

Anyway, it might help to clarify what that denominator means. Why is the "^2" in the parentheses? Perhaps it is easier than I first translated it.
 
x^(3)*e^(2x))dx/[(2x(^2)+1)^(2)]

the ^(2) basically means that the [2xsquared+1] that whole function is squared
 
Not that one. Sorry, I missed the ambiguity of my question.

2x(^2) is my question. Is that 2*x^2 or (2x)^2

Not that it makes a big difference.
 
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