The "perfect infinitive" is a compound tense formed using the formula below:

haber + the past participle = perfect infinitive

Example: the past participle of hablar (to speak) is hablado.
haber + hablado = haber hablado

Example: the past participle of terminar (to finish) is terminado.
haber + terminado = haber terminado

Some example sentences:

Espero haber terminado antes del mediodía.
I hope to have finished by noon.

Gracias por habernos invitado.
Thank you for having invited us.

Since the infinitive auxiliary verb is unconjugated, the past infinitive is the same for all subjects. In addition, the past participle is invariable.

Quisiera haber salido... - I want to have departed...
Ella quisiera haber salido... - She wants to have departed...
Quisiéramos haber salido... - We want to have departed...