I am trying to solve the following integral which supposedly cannot be solved by "normal" means.
$$ \int x^xdx $$
Here's what I've come up with so far:
This must mean that:
this means: $$ x^x-\int x^x\ln(x)dx=\int x^xdx $$
If I can solve $$ \int x^x\ln(x)dx$$
I can solve $$\int x^xdx$$
Any ideas on how to solve the integral? Thanks in advance.