Could $\int\frac{1}{x^{N+1}(x-1)}dx$ be solved analytically? I am trying to solve this integral: 
$$\int\frac{1}{x^{N+1}(x-1)}dx$$
I have tried integration by partial fraction, substitution and by parts. But, I can't solve it. So, I would like to ask could this  be solved?
Also, May I know when partial fraction does not exist? 
Thank you very much. 
Update:
N is any number that is greater than 0. Sorry for forgetting to include such information, and apology for any inconvenience caused. 

Hint:
Assuming that $N$ is natural, you may do the following
$$\int\frac{1}{x^{N+1}(x-1)}dx = \int\frac{1-x^{N+1}+x^{N+1}}{x^{N+1}(x-1)}dx$$
$$= -\int \frac 1{x^{N+1}}\sum_{n=0}^Nx^n \; dx + \int \frac{dx}{x-1}$$
The first sum comes from
$$\frac 1{x^{N+1}}\frac{1-x^{N+1}}{x-1}=-\frac 1{x^{N+1}}\frac{x^{N+1}-1}{x-1}=-\frac 1{x^{N+1}}(1+x+\cdots + x^N)$$
Basically, the above is the partial fraction decomposition of the integrand.
