Improper Integral Converging or Diverging?

Question

For the integral I = 1/(1+x)^e how do we known if it converges or diverges. Upper Limit of 0 and lower limit of -1.

I know that it is improper - is it unbounded at x=-1?

My understanding is that this integral diverges as N approaches -1 from above. Does the function become undefined?

Thanks

Answer 1

$$\int_{-1}^0 {dx\over (1 + x)^e} = \int_0^1{dx\over x^e}$$ What happens at 0?