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(x*Sqrt[5 + 3*x^2])/2 + (5*ArcSinh[Sqrt[3/5]*x])/(2*Sqrt[3])


Integrate[Sqrt[5 + 3*x^2], x] ==
(x*Sqrt[5 + 3*x^2])/2 + (5*ArcSinh[Sqrt[3/5]*x])/ (2*Sqrt[3])



                      2
Integrate[Sqrt[5 + 3 x ], x] == 

                                  3
              2    5 ArcSinh[Sqrt[-] x]
x Sqrt[5 + 3 x ]                  5
---------------- + --------------------
       2                2 Sqrt[3]

Time to compute: 0.02 second

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