Question

∫ x^x dx = ?

Answer 1

+C

Answer 2

The solution is not an elementary function
http://en.wikipedia.org/wiki/Antiderivative

Answer 3

The indefinite integral also has some unknown constant. This can be proven by completing the opposite operations. (derivative) in which C would go to 0. The value of C can be found in cases when an initial condition of the function is given.

Answer 4

Interestingly (for me ...:( ), the definite integral:

∫ x^x dx from 0 to 1 has a very pleasing answer (in the form of a series).

[Sorry for the crude description, I would use LaTeX but it isn't working for me right now]