Purity

Either the first or second time Farkas or Vilkas is spoken to after completing Glory of the Dead, they will ask for help on a quest of a personal matter. They will request that the Dragonborn go with them back to Ysgramor's Tomb and perform the same ritual that was done with Kodlak in order to cleanse themselves of the beast blood.

Objectives

 * Cleanse Vilkas and/or Farkas of his beast blood.

Requirements

 * Must have at least one Glenmoril Witch Head in inventory.
 * Must complete at least one Radiant Quest from Farkas or Vilkas, after completing Glory of the Dead with Glenmoril Witch Head(s) in the inventory.

Walkthrough
After completing Glory of the Dead, return to Jorrvaskr and talk with either Farkas or Vilkas. Instead of offering the usual radiant quests, they will ask for help cleansing themselves of their beast blood.

The Dragonborn must have the Glenmoril Witch head(s), (see "Blood's Honor"), in the inventory before accepting a radiant quest, or "Purity" will not be available.

The quest is relatively easy, as the shortcut to the final room is already open and allows for easy access. The only enemy in the quest is Farkas's/Vilkas's wolf spirit, unless the tomb has not been previously completely cleared by the player.

Once the quest is over, Farkas/Vilkas will be cured of their lycanthropy and will offer the usual radiant quests.

Trivia

 * If the witch heads are stored somewhere and then retrieved after completing a few radiant quests, "Purity" will not show up immediately when talking to Farkas or Vilkas. The Dragonborn must first complete a radiant quest from each of them, with the witch head(s) in the inventory to make "Purity" available.
 * When asking for a job from either Vilkas or Farkas, if they have the option, "Is there any work to be done?", they may offer this quest.

Bugs
Очищение (Skyrim)