Integrate? #int((log(1+x))^3)/(2x)dx#

1 Answer
Truong-Son N.
May 4, 2018

What I see is that #1/x# is the derivative of #lnx#, so I would rewrite this in terms of #ln(u)#.

#log(1+x) = (ln(1+x))/(ln 10)#

As a result:

#=> int (log(1+x))^3/(2x)dx = 1/(2(ln10)^3) int (ln(1+x))^3/xdx#

This has no elementary exact solution, and this is as far as we can go. Had it been #2(1+x)# instead, then this would be doable via #u# substitution.

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