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Hello- can anyone help me with the following problem? Integrate: [(x^e)*(e^x)] dx

MIT 18.01 Single Variable Calculus (OCW)
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So you'll do integration by parts. What do you think is your u, du, and dv?
u=x^e , du=? I also know that the deriv of e^x is equal to e^x. I don't know what the deriv of x^e is ans how to apply u-sub in this case.
Well we can integrate x^e, it's \[\frac{x^{e+1}}{e+1}\] From there you just continue the steps you would normally use. I've never seen this problem before, and I did not see any integral tables with anything that looked like this. So my best guess is this is a similar problem to e^xcosx dx, if you have never tried that problem I would suggest doing that first and see if you get any ideas from that. Hopefully that can help you get started.

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Thank you-this helps alot. Also, I just looked at the problem and the two quantities are added and not multiplied by each other.
Ah! Well that makes the problem a lot easier. Good luck!
Thank you again.

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