I came across an integral involving Bessel function in the denominator, derivatives of Bessel functions and complex argument.The equation yields: $$ \int_0^1 \frac{1}{(1-x^2)[H_{n}^{(1)}(\sqrt{1-x^2}a)]'[H_{n}^{(2)}(\sqrt{1-x^2}a)]'}dx=\int_0^1f(x)dx ,. $$ or the equation could be expressed using Bessel functions as: $$ \int_0^1 \frac{1}{(1-x^2)\{[J_{n}'(\sqrt{1-x^2}a)]^2+[Y_{n}'(\sqrt{1-x^2}a)]^2\}}dx\,. $$ H, J and Y are Hankel function, bessel function and Neumann function,respectively.a is a known constant.
I turned to books but failed to find similar integrals involving bessel function in the denominator. But the plots of f(x) convinced me that it is possible to get an analytical solution. The function be integrated in MATLAB is found as:
Experts on math, could you please tell me how I could do to solve this integral.