Complete the indicated task to learn the corresponding spell.

Expiliarmus: Learned by completing a task for Fred and George
Insendio: Learned by completing a task.
Levicorpus: Learned from Hermione after finishing all the tasks and the class with Snape. Go to Room Of Recruitment. AD will ask you for a funny spell and Hermione will teach it to you.
Petrificus Totalus: Learned from Hermione when you try to help one of brothers Krivi. When you finish his task, talk to him at the Room Of Recruitment.
Protego: Learned from Hermione during a task to help Nevil.
Reducto: Comlete Jini's task then go to the Room Of Recruitment and talk to her.
Rictumsempra: Learned from Hermione when you try to help Zaharia. When you finish his task, talk to him at The Room Of Recruitment.
Stupify: Learned by completing a task for Fred and George.