I need to integrate Sqrt[Cos(x)+(Cos(x))^3] Mathematica gives answer with AppelF, I've never heard about it. This excercize was given in my book, so there must be answer in elementary functions. I tryed 1) tg(x/2)=t and 2) Cosx=t , but both didn't help me. Give me please any advice. What does AppelF mean?