Question on integration of $x^{x}$ I want to evaluate $\displaystyle\int x^{x} \, dx$.
For this I am taking 
$$\begin{align}
x^{x}&=t\\
\log {x^{x}}&=\log {t}\\
x\log x&=\log t\\
e^{x\log x}&=t\\
\end{align}$$
Then I am stuck! Please make suggestions on how to do this example.

See Power Tower for a note on how $x^x$ has not indefinite integral in terns of elementary functions, but the definite integral $\int_0^1 x^x dx$ does have an answer.
