Question:Tough BesselJ Integral

Question:Tough BesselJ Integral

Maple 2015

Hi,

I have a list of 603 integrals that I want to evaluate. Unfortunately, I can't get Maple to do most of them. Mathematica can do some that Maple can't, and returns an answer in terms of BesselJ functions. So my question is 2-fold

1) Is there a way to make Maple do this integral?
2) If not, is there a way to efficiently convert 603 expessions to Mathematica and back?

EXAMPLE INTEGRAL
restart;
assume(k1::real, k2::real, R::real, R>0);
a :=cos(x)*exp(I*(k1*R*sin(x)+k2*R*sin(x)-4*x))*sin(x):
int(a, x=-Pi/2..Pi/2) assuming real;

Thanks!

 > restart;
 > assume(k1::real, k2::real, R::real, R>0);
 > a :=cos(x)*exp(I*(k1*R*sin(x)+k2*R*sin(x)-4*x))*sin(x)
 (1)
 > int(a, x=-Pi/2..Pi/2) assuming real;
 (2)

 > ans := -(1/((k1 + k2)^6*R^6))*2*I*Pi* ( 10*(k1 + k2)^4*Pi*R^4*BesselJ(2, sqrt((k1 + k2)^2*R^2)) + 2*Pi ((k1 + k2)^2*R^2)^(3/2) (-30 + (k1 + k2)^2*R^2) *BesselJ(3, sqrt((k1 + k2)^2*R^2)) - (k1 + k2)^4*R^4*(-(k1 + k2)*R*cos((k1 + k2)*R) + sin((k1 + k2)*R)) + 8*(k1 + k2)^2*R^2*(-(k1 + k2)*R*(-6 + (k1 + k2)^2*R^2)*cos((k1 + k2)*R) + 3*(-2 + (k1 + k2)^2*R^2)*sin((k1 + k2)*R)) - 8*(-(k1 + k2)*R*( 120 - 20*k2^2*R^2 + k1^4*R^4 + 4*k1^3*k2*R^4 +
 > k2^4*R^4 + 4*k1*k2*R^2*(-10 + k2^2*R^2) +
 > k1^2*(-20*R^2 + 6*k2^2*R^4))*cos((k1 + k2)*R) +
 > 5*(24 - 12*k2^2*R^2 + k1^4*R^4 + 4*k1^3*k2*R^4 + k2^4*R^4 +
 > 4*k1*k2*R^2*(-6 + k2^2*R^2) +
 > 6*k1^2*R^2*(-2 + k2^2*R^2))*sin((k1 + k2)*R) ) );
 (3)
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