1/(3+cos x)的不定积分怎么算?

问题描述:

1/(3+cos x)的不定积分怎么算?

用万能代换,令t=tan(x/2),则cosx=(1-t²)/(1+t²),dx=2dt/(1+t²)∫dx/(3+cosx)=2∫dt/(2t²+4)=∫dt/(t²+2)=√2/2arctan(t/√2)+C=√2/2arctan(tan(x/2)/√2)+C...