令x=3sinadx=3cosada√(9-x²)=3cosaa=arcsin(x/3)sina=x/3则cosa=√(1-x²/9)=√(9-x²)/3所以原式=∫(1-3sina)/3cosa*3cosada=∫(1-3sina)da=a+3cosa+C=arcsin(x/3)+√(9-x²)/3+C
