You can't integrate but you can use power series for to approximate a value for such integral.
Hey I've been having trouble integrating:
Here's what I have tried so far:
But here's where I encounter a problem...I can't break it down properly after I do that substitution ... I just keep getting 0 = 0 or something like that. Am I on the correct path though?
Aha! This makes more sense!
As a first solution, we can easily tackle this with double integration.
Consider Besides We're going to create a double integral, and of course, the only reason that I'd ever create a double integral that wasn't there in first place is so I could reverse integration order. (This is justified by Tonelli's Theorem.)
Since the function we're tryin' to integrate is even, after insert the parameter and reverse integration order we have:
Now let's make this easier with complex numbers:
Hence and the rest follows.
Yeah we definitely haven't done Euler's yet ... but I guess that explains why this in on the wall in my engineering lounge:
Yeah my question gave us the hint of Integration by parts...but that didn't help me at all.
I like this answer much more. I might not actually hand it in just because it's obviously something we wouldn't know yet. But it's still interesting to know.