∫1/(2+sinx)dx做代换tgx/2=t则sinx=2t/(1+t^2)dx=d(2arctgt)=2dt/(1+t^2)∫1/(2+sinx)dx=∫[2/(1+t^2)]/[2+2t/(1+t^2)]dt=∫2/(2(1+t^2)+2t)dt=∫1/(t^2+t+1)dt=∫1/[(t+1/2)^2+3/4]dt=4/3∫1/{[(2t+1)/√3]^2+1}=2...