# 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 ,