Help for evaluating complicated integral $\int \frac 1 {x^n-x} dx$ I have this complicated integral to evaluate :
$$\int \dfrac 1 {x^n-x} dx$$
I'm struggling to evaluate this.
My attempt :
$$\int \dfrac1x \cdot \dfrac 1 {x^{n-1}-1} dx$$ 
Now, I try to apply integration by parts. For that, I use : $V=\large\dfrac1x$ and $U=\large\dfrac 1 {x^{n-1}-1}$
But, that doesnt take me anywhere. It just gives me an even more complicated expression to evaluate..
Help would be appreciated.. Thank you..

$$\int\dfrac{1}{x^n-x}\mathrm{d}x=\int\dfrac{1}{x^n\left(1-\dfrac{1}{x^{n-1}}\right)}\mathrm{d}x$$
Now subs. $\dfrac{1}{x^{n-1}}=t\implies \mathrm{d}t=-\dfrac{(n-1)}{x^n}\mathrm{d}x$
Hence your integral becomes $$\dfrac{1}{(n-1)}\int\dfrac{\mathrm{d}t}{t-1}$$
