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$x*HypergeometricPFQ[{1/2}, {1, 3/2}, -x^2/4]$

Integrate[BesselJ[0, x], x] ==

                                   2
                     1       3   -x
x HypergeometricPFQ[{-}, {1, -}, ---]
                     2       2    4

Time to compute: 0.02 second

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