What is the best approach for solving the integral of x*e^cos(x) from 0 to 6?

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SUMMARY

The integral of x*e^cos(x) from 0 to 6 cannot be solved analytically using standard techniques such as integration by parts or De Moivre's theorem. Participants in the discussion concluded that numerical methods are the only viable approach to obtain a solution. Tools like Wolfram Alpha can provide a numeric approximation, which is recommended for practical purposes. The consensus emphasizes that complex integration methods are not applicable for this integral.

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Homework Statement



integral of x*e^cos(x) from 0 to 6.

Homework Equations



I tried using integration by parts twice but no luck (couldn't find the integral of e^cos(x)). I was hoping I might use De Moivre's theorem but don't think it's applicable. I thought this looked a little like a La Place Transform, but couldn't find the appropriate form. Thought about integrating over a complex region, but forgot how and don't have 20 free hours to figure it out. I almost stated reading about the LeBesgue which I never understood in the first place.

The Attempt at a Solution



I punched it into wolfram alpha with some bounds and I finally got a numeric solution. What am I not seeing here, it's driving me crazy. Am I just supposed to use a graphing utility to solve this within as many significant digits that I care to compute?
 
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It looks like your only choice is a numerical solution. I don't see any other way to do it.
 
I must agree with Dick, a numerical solution is the only option I see.

** Before you go looking at complex integration - it can't be done with it's methods.
 
Alright, I appreciate the help guys.
 

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