Question on integration of $x^{x}$

Question

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.

for bound $0-1$ this does have interesting property. Check this out — S L, Mar 19 '13 at 06:03
As indicated by Potato this integral is not elementary : see this thread. — Raymond Manzoni, Mar 19 '13 at 08:01

score 3 · Answer 1 · answered Mar 19 '13 at 06:22

3

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.

answered Mar 19 '13 at 06:22

Question on integration of $x^{x}$

1 Answers1