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Integrate[Sqrt[1 + E^(5*x) + E^(10*x)], x] ==
Sqrt[1 + E^(5*x) + E^(10*x)]/5 + x + ArcSinh[(1 + 2*E^(5*x))/Sqrt[3]]/10 - Log[5*(2 + E^(5*x) + 2*Sqrt[1 + E^(5*x) + E^(10*x)])]/5

                    5 x    10 x
Integrate[Sqrt[1 + E    + E    ], x] == 

                                            5 x
                                     1 + 2 E
          5 x    10 x        ArcSinh[----------]
Sqrt[1 + E    + E    ]                Sqrt[3]
---------------------- + x + ------------------- - 
          5                          10
 
              5 x               5 x    10 x
  Log[5 (2 + E    + 2 Sqrt[1 + E    + E    ])]
  --------------------------------------------
                       5