Time for capacitor charging in RLC circuit
At one extreme, RC is exactly what it is for the example without L or a very small value of L. As L becomes more dominant, things change: -



So, the blue curve is a small value of L. The pink/magenta curve is the case when the value of L is sufficient to cause a little overshoot and the green condition is when L and C are more dominant than R. It's all about ratios.

This might make useful reading on the topic.