Question 1162608
.
<pre>

It is  {{{(n(n+1)/2)*log(x)}}},  INSTEAD.
</pre>


<H2>Fix the error in your post (!)</H2>


<pre>
It is the sum of the arithmetic progression


    log(x) + 2*log(x) + 3*log(x) + . . . + n*log(x) = log(x)*(1 + 2 + 3 + . . . + n) = {{{(n(n+1)/2)*log(x)}}}.
</pre>

Solved.