I need more help

1. Apr 24, 2005

abia ubong

i came acreoss a problem thats red like this ,wats the integral of x^x i gev it all i could so can anyone help me,furthermore wats the integral ,of a fuction raised 2 another e.g x^x,e^[x^2],cos[x]^[sin[x].and so on

2. Apr 24, 2005

dextercioby

One of them,viz.$\int \mbox{exp} \left(x^{2}\right) \ dx$,can be expressed as function of the "common" special functions (the erf of imaginary argument).The other that u mentioned cannot...

Daniel.

3. Apr 24, 2005

HallsofIvy

Staff Emeritus
Where are you getting these problems? None of these functions can be integrated in terms of elementary functions.

4. Apr 25, 2005

dfollett76

Just a quick thought: what about breaking x^x into a product. For instance x^x = [x^(x-1)]*x^1 and then try integration by parts. It's been a while since my calculus days but that sounds like something I might have tried.

5. Apr 25, 2005

dextercioby

It's usless.Here's why.

$$\int x^{x} \ dx =\int x^{x-1} x \ dx=\frac{x^{x-1}x^{2}}{2}-\frac{1}{2}\int x^{x-1}\left[x(x-1)+x^{2}\ln x\right] \ dx$$

and the second integral looks horrible...

Daniel.

6. Apr 27, 2005

abia ubong

hey thnxs for all but they still do not help ,