Thanks for the tip! :)

I don't know anything about Bessel functions.  What are they?  And btw, no
I'm not sure about anything regarding this :)

When I was searching for the integrals, (and I'm not very exprienced) I
tried simplifying the integral into something I knew how to deal with.   I
also tried to integrate simpler [looking] integrals that had something in
common with the actual integral I wanted to integrate.   The integral of
cos( sin(x) ) dx was one of the latter.

The other thing I wanted to ask you is where can I get information about
Gradstein/Ryshik and Abramowitz/Stegun and Runge Kutta?  I'm very much a
novice...
    -Charles

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