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-(Pi*x*HypergeometricPFQ[{1/2, 1, 1, 3/2}, {2, 2, 2}, x])/8 - (Pi*x*HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, x])/8

Integrate[(EllipticE[x] - EllipticK[x])/x, x] ==
-(Pi*x*HypergeometricPFQ[{1/2, 1, 1, 3/2}, {2, 2, 2}, x])/8 - (Pi*x*HypergeometricPFQ[ {1, 1, 3/2, 3/2}, {2, 2, 2}, x])/8 

          EllipticE[x] - EllipticK[x]
Integrate[---------------------------, x] == 
                       x

                          1        3
-(Pi x HypergeometricPFQ[{-, 1, 1, -}, {2, 2, 2}, 
                          2        2
 
       x]) / 8 - 
 
                                 3  3
   Pi x HypergeometricPFQ[{1, 1, -, -}, {2, 2, 2}, x]
                                 2  2
   --------------------------------------------------
                           8
Time to compute: 1.45 second
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