Mercury's Orbital Precession Anomaly

[Bjarne]

The perihelion of Mercury precesses by 5600 arc-seconds per century, which is 43 arc-seconds per century more than Newtonian physics alone would predict

Albert Einstein proposed a second-order correction to Mercury's orbit, based on his general theory of relativity.

Which equation had Einstein used to calculate this?

 

[Nabeshin]

The equation one gets from the analysis is, I believe (lifted from Hartle):
$$\Delta \phi = 2 l \int_{r_1}^{r_2}\frac{dr}{r^2}\left(1-\frac{2GM}{r c^2}\right)^{-1/2}\left[c^2 e^2 \left(1-\frac{2GM}{r c^2}\right)^{-1} - \left(c^2 + \frac{l^2}{r^2}\right)\right]^{-1/2}$$
I don't have the book in front of me though so there might be small errors.
One can expand this to get a definite answer neglecting higher order corrections, but I don't have that equation in front of me.