  Through this article, I will overview the use of Noether symmetry approach in
discussing the integration of geodesic equations for the geodesic Lagrangians
of spacetimes. I will also give some examples to reveal the efficiency of
Noether symmetry approach by finding the first integrals related for the
geodesic Lagrangians of the G\"{o}del-type, Schwarzschild,
Reissner-Nordstr\"{o}m and Kerr spacetimes. After obtaining the approximate
Noether symmetries of the Schwarzschild, Reissner-Nordstr\"{o}m and Kerr
spacetimes, the first integrals associated with each of approximate Noether
symmetries have been integrated to find a general solution of geodesic
equations in terms of the arc length $s$.
