Evaluate: `intx^x1n(e x)dx`

Answer

`x^(x)+C`

Explanation

`I=int x^(x) " In "(ex)dx=int x^(x) (1+"In "x)dx`
` "Let "t=x^(x)=e^(x"In"x)" then " (dt)/(dx)=x^(x)(x xx (1)/(x)+"In "x)`
` or dt=x^(x)(1+"In "x)dx or I=intdt=t+C=x^(x)+C`