Re: integral of a^sin(x)

For the integral from 0 to pi in the case a = e, Mathematica gives

pi * ( I_0(1) + L_0(1) )

where I_0 is a modified Bessel function of the first kind and L_0 is a
Struve L-function. So the answer is, "No, there isn't an algebraic
expression." If you plot the integral it looks sort of like a wavy
diagonal line.

.

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