Integrate $\int\frac{x^3+1}{x^4+x^3+x^2+x}\,dx$ How do I integrate $\displaystyle\int\dfrac{x^3+1}{x^4+x^3+x^2+x}\,\mathrm dx$?
I tried by splitting the equation in two parts like $\dfrac{x^3}{x^4+x^3+x^2+x}$ and $\dfrac1{x^4+x^3+x^2+x}$ and then cancelling out the $x$ terms from the first part and then trying to integrate further.
But this did nothing much to it, and also the other part became more difficult to solve. 
How do I solve this integration?

Hint:
$$\dfrac{x^3+1}{x^4+x^3+x^2+x}=\dfrac{1}{x}-\dfrac{1}{x^2+1}$$
