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Integrate[x*Coth[Sqrt[2] - x], x] ==
(2*Sqrt[2]*x - I*Pi*x - x^2 + 2*(Sqrt[2] - x)* Log[1 - E^(2*Sqrt[2] - 2*x)] + I*Pi*Log[1 + E^(2*x)] - I*Pi*Log[Cosh[x]] - 2*Sqrt[2]*Log[(-I)*Sinh[Sqrt[2] - x]] + PolyLog[2, E^(2*Sqrt[2] - 2*x)])/2



Integrate[x Coth[Sqrt[2] - x], x] == 

                         2
(2 Sqrt[2] x - I Pi x - x  + 
 
                             2 Sqrt[2] - 2 x
    2 (Sqrt[2] - x) Log[1 - E               ] + 
 
                  2 x
    I Pi Log[1 + E   ] - I Pi Log[Cosh[x]] - 
 
    2 Sqrt[2] Log[-I Sinh[Sqrt[2] - x]] + 
 
                2 Sqrt[2] - 2 x
    PolyLog[2, E               ]) / 2

Time to compute: 0.28 second

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