I have shown that:

When $\displaystyle \rho = \beta + i \gamma$

Then

$\displaystyle \frac{x^{\rho}}{\rho} +\frac{x^{\overline \rho}}{\overline\rho} = \frac{2x^{\beta}}{|\rho|} cos(\gamma In(x) - \theta)$

However I don't how I can explain why:

$\displaystyle Li(x^{\rho}) \sim \frac{x^{\rho}}{\rho Inx}$