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

[Daveyboy]

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?

 

[Dick]

It looks like your only choice is a numerical solution. I don't see any other way to do it.

 

[gomunkul51]

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.

 

[Daveyboy]

Alright, I appreciate the help guys.