I was sitting and decided to get a precise magnetic field equation from Bio-Savar law, and got out this handsome formula (by the way, is there a way to use ASCIIMath here on Mathematics?): $$ \vec{B}(x,y,z)=\frac{\mu_0I}{4\pi}\int_{0}^{\frac{2\pi L}{d}}\frac{\begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ -R\sin t & R\cos t & \frac{d}{2\pi} \\ x-R\cos t & y-R\sin t & z-\frac{td}{2\pi} \end{vmatrix}}{\sqrt{(x-R\cos t)^2+(y-R\sin t)^2 +\left(z-\frac{td}{2\pi}\right)^2}^3}\,\, dt $$ Maxima opened a determinant for me, but it didn't take an integral, maybe because this is quite complex thing to integrate. Is there a way I can take this integral using free computer algebra systems? If yes, what program should I try?
After some time: Decided to use numerical methods, I will take the concrete solenoid lengths, radiuses, coil thicknesses and coordinates and read wiki for other methods of calculation of the flux density in real solenoids.