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**davesface** I need to integrate $\displaystyle \int5e^{x}sin\left(2x \right)dx$, and I just cannot figure out what the trick is to it. I don't think it's any combination of integration by parts since $\displaystyle e^{x}$ will always stay the same and the other function will oscillate back and forth between sin and cosine, and all that will happen is that the factors of 5 will increase.

I also tried the double angle identity $\displaystyle sin(2x)=2sin(x)cos(x)$, and that resulted in the same kind of loop. I'm sure it's some little trick that I'm missing here, so any hints would be greatly appreciated.