1. Integrate x^(x)

What is the definite integral of x^(x)
from 0 to 1?

2. Re: Integrate x^(x)

Originally Posted by nycmath
What is the definite integral of x^(x)
from 0 to 1?
There's no closed form for this. A quick google show's you're not the first to run up against this function.

Numerically it integrates to roughly 0.783431.

3. Re: Integrate x^(x)

As usual for special functions, there is no closed form until a closed form is defined and referenced.
"The Sophomores Dream Function" on Scribd : JJacquelin's Documents | Scribd
Sphd(1;x) is an antiderivative of x^x .
Before saying "This is a vicious circle", one have to think at the role played by all special functions in maths. On this subject, the paper : "Safari in the country of special functions", pp.18-36, same link on Scribd.