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2*Sqrt[1 + E^x] + (2*(1 + x)^(3/2))/3 - 2*ArcTanh[Sqrt[1 + E^x]]

Integrate[Sqrt[1 + E^x] + Sqrt[1 + x], x] ==
2*Sqrt[1 + E^x] + (2*(1 + x)^(3/2))/3 - 2*ArcTanh[Sqrt[1 + E^x]] 

                    x
Integrate[Sqrt[1 + E ] + Sqrt[1 + x], x] == 

                          3/2
            x    2 (1 + x)
2 Sqrt[1 + E ] + ------------ - 
                      3
 
                      x
  2 ArcTanh[Sqrt[1 + E ]]
Time to compute: 0.04 second
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