I am sorry to fail to give a mathematical expression. Maybe  you can try to use numerical method for an specific case.

I am able to solve this equation but only for a = 0. for this case, the equation reduces to similar as 6.633 eq in table of integrals book by Ryzhik . But, in my case a is not zero. Please help if any body can do ?

I can give some hints (maybe you have gone through them):

1) Use the Bessel function of the first kind as series expansion (https://en.wikipedia.org/wiki/Bessel_function);

2) Change the integration variable to x^2 as: xdx = (1/2) d(x^2);

3) Use the Binomial formula for (x^2+a^2)^m (https://en.wikipedia.org/wiki/Binomial_theorem);

4) Then, the Euler integrals of the second kind (https://en.wikipedia.org/wiki/Euler_integral).

I hope it helps.