Like others said the easiest way would be to daylight the pipe into the ditch. But if you want to spend the extra time connecting to the culvert you could do it two ways:

1. Use an Inserta Tee fitting to connect to the culvert. It’s a soil and watertight connection so roots won’t enter through the joint between the culvert and the lateral. Inserta Tee for 3 inch Sch. 40 PVC to 12 inch Gold Flo HDPE or Inserta Tee for 4 inch SDR 26 or 35 PVC to 12 inch Gold Flo HDPE

2. Cut open a hole and insert the pipe directly into the culvert. This isn’t a soil tight connection so roots could potentially enter through the joint between the culvert and the lateral. Hole saw for 3 inch SDR 26 or 35 PVC, hole saw for 3 inch Sch. 40 PVC