1/(sinx+cosx)的定积分怎么求

问题描述:

1/(sinx+cosx)的定积分怎么求

用万能代替∫1/(sinx+cosx)dx=∫1/{2tan(x/2)/[1+tan^2(x/2)]+[1-tan^2(x/2)]/[1+tan^2(x/2)]}dx=∫[1+tan^2(x/2)]/[2tan(x/2)+1-tan^2(x/2)]dx=-∫1/[-2tan(x/2)-1+tan^2(x/2)]dtan(x/2)=-∫1/{[tan(x/2)-1]...