Integral that MAPLE could not evaluate

[tsunamiBTP]

I have attached a pdf of output from MAPLE attempting to evaluate an integral of an exponential function containing a complex irrational trig function as the exponent. MAPLE could not evaluate it when integrating with respect to the hangle phi. I then transformed the integral via varible substitutions to hopefully get it in a form that might be executable, but no luck there either.

Any suggestions?

This integral is a portion of a solution of a radiation wave emanating in the vicinity of source that is configured as a disc.

 

[HallsofIvy]

That looks to me like a variation on an elliptic integral.

 

[g_edgar]

There is no reason to think this integral has a closed form evaluation.

 

[tsunamiBTP]

Is g_edgar suggesting that this integral can only be evaluated numerically for specific values for r & theta?