hi all
please could you help me how do we integrate this integration in the attachment the answer is bessel function the integration is for loop antenna

thanks

Let $\phi'=A, \phi=B$

$cos(2A)= cos^2A-sin^2A$
$cos(2A)+1= cos^2A-sin^2A+1= 2cos^2A$

$cos(B-A)= cosBcosA-sinBsinA$

Let $jka.sin(\theta)=t$
$e^{t(cos(B-A)}= e^{t(cosBcosA-sinBsinA)}=e^{t(cosBcosA)}\cdot e^{t(sinBsinA)}$

Now try to integrate

$2cos^2(A)\cdot(e^{t(cosBcosA)}\cdot e^{t(sinBsinA)})dA$

thanks
but how you could integrate the remaining it
is difficult