I am trying to evaluate this indefinite integral: $$\int \frac{x+1}{(x^2+1) \sqrt{x^2-6x+1}} dx$$ What I tried
- Substitution $u = \arctan(x)$. However, no luck after this
- Find substitutions to convert $x^2 - 6x + 1$ into $(a + bu)^2$ or $a - (b + cu)^2$, however I could not find any
- Converted $x^2 - 6x + 1$ into $(x-3)^2 - 8$ and used the derivative of $\sec^{-1}{(x)}$ but not any luck after that as well.
- I suspect that it has a real solution, so the solution from wolfram alfa is not what I am looking for.
Any help/solutions would be very much appreciated!