定积分∫(-π/2到π/2)(sin(x+π/6))/((sinx)^2)+1)dx=

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定积分∫(-π/2到π/2)(sin(x+π/6))/((sinx)^2)+1)dx=
定积分∫(-π/2到π/2)(sin(x+π/6))/((sinx)^2)+1)dx=

定积分∫(-π/2到π/2)(sin(x+π/6))/((sinx)^2)+1)dx=
∫(-π/2到π/2)(sin(x+π/6))/((sinx)^2)+1)dx
=∫(-π/2到π/2)(sinxcosπ/6+cosxsinπ/6))/((sinx)^2)+1)dx (第1部分是奇函数,积分=0)
=∫(-π/2到π/2)(sinπ/6))/((sinx)^2)+1)dsinx
=arctansinx |(-π/2到π/2)
=π/2