Mathematica: Obtain moments of random variableXXgivenEXlog(1+etX)EXlog(1+etX)

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Obtain moments of random variableXXgivenEXlog(1+etX)EXlog(1+etX)
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(mathematica.stackexchange.com/users/217/yaroslav-bulatov)Yaroslav Bulatov
(mathematica.stackexchange.com/users/62063/a-kato)A. Kato
(mathematica.stackexchange.com/users/19758/jimb)JimB
(mathematica.stackexchange.com/users/9469/yarchik)yarchik
(mathematica.stackexchange.com/users/19758/jimb)JimB
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