How would I integrate exp(x)*cos(x)

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Homework Help Overview

The problem involves integrating the function exp(x) * cos(x), where exp refers to Euler's number. The discussion revolves around various integration techniques and their effectiveness in this context.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the ineffectiveness of u-substitution and explore integration by parts as a potential method. Some suggest using complex exponentials as an alternative approach, while others express concerns about the complexity of this method.

Discussion Status

The discussion is active, with participants sharing different methods and expressing varying opinions on their effectiveness. There is no clear consensus, but multiple approaches are being considered, indicating a productive exploration of the problem.

Contextual Notes

Participants note the challenges associated with simplifying the results from the complex exponential method, as well as the potential pitfalls in integration by parts.

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Homework Statement



How would I integrate exp(x)*cos(x), exp is referring to euler's number

Homework Equations





The Attempt at a Solution



u substitution doesn't work
 
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Hi ComFlu945! :smile:

Integrate by parts twice, and then use a bit of ingenuity. :wink:
 
What would you even substitute? :eek: Well, I guess there are two or three things to try -- and you saw none of them worked out.

What other methods do you know?
 
e^x \cos x =\Re \, e^{(1+i)x} which integrates nicely.
 
Isn't that a bit complex (pun?) though?

I'd just do the integration by parts thing.
 
benorin said:
e^x \cos x =\Re \, e^{(1+i)x} which integrates nicely.

Yes, it's a nice trick, and it integrates nicely, but then you've got to simplify it, which is awkward and easy to get wrong. :redface:
 
Not to mention it let's you avoid this wonderful exercise that reminds us of something that is often forgotten...
 

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