Evaluate $\int \frac{x+1}{(x^2-x+8)^3}\, dx$ Could you give me a hint on how to find $$\int \frac{x+1}{(x^2-x+8)^3}\,  dx$$
It doesn't seem like partial fractions are the way to go with here and using the integration by parts method seems to be tedious.
I have also tried substituting $(x^2-x+8)$ but it gets even more complicated then. 
Is there a way to solve this using only basic formulas?

If you multiply the top by two and then add and subtract 1 you can split the integral up as ∫2x - 1 / (x^2 - x + 8)^3  dx + ∫ 3 / (x^2 - x + 8)^3  dx  
