积分1/(3+2cosx)等于

Question

积分1/(3+2cosx)等于

Answer 1

1/(3+2cosx)=1/[1+2(1+cosx)]=1/[1+4cos^2(x/2)]=sec^2(x/2)/[sec^2(x/2)+4]=sec^2(x/2)/[tan^2(x/2)+5]∫ 1/(3+2cosx) dx=∫ [sec^2(x/2)dx]/[tan^2(x/2)+5]=2∫ [dtan(x/2)]/[tan^2(x/2)+5]=2/√5 arctan[tan(x/2)...