Difficult integral by sub., parts & table

1. The problem statement, all variables and given/known data
[tex]\int xe^{2x^2} cos(3x^2) dx[/tex]
This is the hardest integral I've attempted so far. I've come up with an answer that fits a table in my book but I'm not sure if I arrived there correctly. Thanks for reading!

2. Relevant equations
[tex]\int e^{au} cos\ bu\ du\ = \frac{e^{au}}{a^2+b^2}(a\ cos\ bu\ + b\ sin\ bu)+C[/tex]

3. The attempt at a solution


[tex]du=2x dx[/tex]

[tex]I=\int xe^{2x^2}\cos(3x^2){\rm dx}\,=\, {1\over 2} \int e^{2u}\cos(3u) {\rm du}[/tex]

I have done some shortcut here, with use of the formula, your number two:

[tex]I={1\over 26} e^{2u} (2 \cos(3u)\,+\,3\sin(3u))\,+\,C [/tex]

[tex]I={1\over 26} e^{2x^2} (2 \cos(3x^2)\,+\,3\sin(3x^2))\,+\,C [/tex]

this is the same as integrator...


check it out
Here's the solution, I didn't simplify it any more like I should have, but I hope you understand the basic process. I checked my answer with CAS and it's correct, so don't worry about that.
http://img411.imageshack.us/img411/5615/file0001su6.jpg [Broken]
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Thanks alot!

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