Question: Tough BesselJ Integral

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)

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;

int(cos(x)*exp(I*(k1*R*sin(x)+k2*R*sin(x)-4*x))*sin(x), x = -(1/2)*Pi .. (1/2)*Pi)

(2)

Mathematica Answer

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)
)
);

-(2*I)*Pi*(10*(k1+k2)^4*Pi*R^4*BesselJ(2, (k1+k2)*R)+2*Pi((k1+k2)^2*R^2)^(3/2)*BesselJ(3, (k1+k2)*R)-(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*R^2*k2^2+k1^4*R^4+4*k1^3*k2*R^4+k2^4*R^4+4*k1*k2*R^2*(R^2*k2^2-10)+k1^2*(6*R^4*k2^2-20*R^2))*cos((k1+k2)*R)-40*(24-12*R^2*k2^2+k1^4*R^4+4*k1^3*k2*R^4+k2^4*R^4+4*k1*k2*R^2*(R^2*k2^2-6)+6*k1^2*R^2*(R^2*k2^2-2))*sin((k1+k2)*R))/((k1+k2)^6*R^6)

(3)

 

 


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