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(4*x - Sqrt[2]*Log[4*Sqrt[2] - 4*Sin[2*x]] + Sqrt[2]*Log[Sqrt[2] + Sin[2*x]])/8

Integrate[1/(1 + Tan[x]^4), x] ==
(4*x - Sqrt[2]*Log[4*Sqrt[2] - 4*Sin[2*x]] + Sqrt[2]*Log[Sqrt[2] + Sin[2*x]])/8 

               1
Integrate[-----------, x] == 
                    4
          1 + Tan[x]

(4 x - Sqrt[2] Log[4 Sqrt[2] - 4 Sin[2 x]] + 
 
    Sqrt[2] Log[Sqrt[2] + Sin[2 x]]) / 8
Time to compute: 0.18 second
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