102.tex

\def\no{102}
\def\theintegral{\(\int{\frac{1}{u\ln{u}}}\;\dif{u}%
\enspace=\enspace%
\ln\abs{\ln{u}}\;+\;C\)}

\begin{align*}
%
{I}_{\no}
=&  \int \frac{1}{u\ln u} \dif u
\nb\sub[\quad
v = \ln u
\andso \dif v = \frac{1}{u} \dif u
]%
%
=&  \int \frac{1}{v} \dif v
\\
=&  \ln v + C
\nb\unsub
=&  \ln\abs{\ln u}
%
\end{align*}