I'm trying to understand the calculation here: http://en.wikipedia.org/wiki/Fraunhofer_diffraction_(mathematics)#Circular_aperture for the solution by integration, but I plain and simple fail to see how I get from the anti derivative $$\int_0^x x'\cdot J_0(x')dx' = x\cdot J_1(x)$$ to $$\frac{J_1(\pi W\rho /\lambda z)}{\pi W\rho /\lambda z}$$ (substituting $x'=\frac{2\pi\rho}{\lambda z}\rho'$), which is basically, reversing the substitution, $\frac{J_1(x)}{x}=jinc(x)$.

Can anyone enlighten me?


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