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(x^5*(2 + 5*Log[2*x]*(-2 + 5*Log[2*x])))/125


Integrate[x^4*Log[2*x]^2, x] ==
(x^5*(2 + 5*Log[2*x]*(-2 + 5*Log[2*x])))/125



           4         2
Integrate[x  Log[2 x] , x] == 

 5
x  (2 + 5 Log[2 x] (-2 + 5 Log[2 x]))
-------------------------------------
                 125

Time to compute: < 0.01 second

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