Can the Risch Algorithm Determine Integrability of Functions Like ∫x^x dx?

[Maths Lover]

if dy/dx = x^x , find y ?

or

find
∫x^x dx

?

 

[HallsofIvy]

That cannot be integrated in terms of elementary functions.

Where did you get that problem?

 

[Maths Lover]

That cannot be integrated in terms of elementary functions.

Is there a way enable us to know that a function F can be intergrated in terms of elementary functions or not ?

 

[micromass]

Is there a way enable us to know that a function F can be intergrated in terms of elementary functions or not ?

It is called the Risch algorithm: http://en.wikipedia.org/wiki/Risch_algorithm