Lösung 2.3:1d
Aus Online Mathematik Brückenkurs 2
We can discern two factors in the integrand,
\displaystyle \begin{align}
& \int{x\ln x\,dx=\frac{x^{2}}{2}\ln x}-\int{\frac{x^{2}}{2}}\centerdot \frac{1}{x}\,dx \\
& =\frac{x^{2}}{2}\ln x-\frac{1}{2}\int{x\,dx} \\
& =\frac{x^{2}}{2}\ln x-\frac{1}{2}\centerdot \frac{x^{2}}{2}+C \\
& =\frac{x^{2}}{2}\left( \ln x-\frac{1}{2} \right)+C \\
\end{align}
Thus, how one should the factors in a partial integration is very dependent on the situation and there are no simple rules.