# Difficult integral by sub., parts & table

## Homework Statement

$$\int xe^{2x^2} cos(3x^2) dx$$
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!

## Homework Equations

$$\int e^{au} cos\ bu\ du\ = \frac{e^{au}}{a^2+b^2}(a\ cos\ bu\ + b\ sin\ bu)+C$$

## The Attempt at a Solution

http://www.mcp-server.com/~lush/shillmud/int2.7.JPG
http://www.mcp-server.com/~lush/shillmud/int2.72.JPG

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substitute:

$$u=x^2$$

$$du=2x dx$$

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

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

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

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

this is the same as integrator...

http://integrals.wolfram.com/

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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How do you submit scanned work onto here?
Thanks

How do you submit scanned work onto here?
Thanks
Assuming the scanned image is in a format the forum recognises, jpeg,mpeg and so on either click on the icon in yellow with a black mountain or two and a black sun, visible in the new reply or go advanced: edit windows, not quick post. Or type [noparse]*url [Broken][/noparse] around the files url.

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Thanks alot!