∫1/√(a^2-x^2)^3dx(a>0)_数学解答

∫1/√(a^2-x^2)^3dx(a>0)

人气：120 ℃　时间：2020-09-17 18:00:59

解答

∫1/√(a²-x²)³dx令x=asinu,则√(a²-x²)=acosu,dx=acosudu=∫1/(a³cos³u) *acosudu=(1/a²)∫sec²udu=(1/a²)tanu+C由x=asinu,则√(a²-x²)=acosu,得：ta...