大佬们，救救救

let
u=-x
du =-dx
I
=∫(-π->π) [xsinx.arctan(e^x)]/[ 1+(cosx)^2] dx
=∫(π->-π) { [usinu.arctan(e^(-u))]/[ 1+(cosu)^2] } (-du)
=∫(-π->π) [xsinx.arctan(e^(-x))]/[ 1+(cosx)^2] dx
2I
=∫(-π->π) [xsinx.arctan(e^x)]/[ 1+(cosx)^2] dx +∫(-π->π) [xsinx.arctan(e^)(-x))]/[ 1+(cosx)^2] dx
=(π/2)∫(-π->π) xsinx/[ 1+(cosx)^2] dx
= π∫(0->π) xsinx/[ 1+(cosx)^2] dx
//let t=π-x
= π∫(π->0) { (π-t)sint/[ 1+(cost)^2] } (-dt)
= π∫(0->π) (π-x)sinx/[ 1+(cosx)^2] dx
4I
=π∫(0->π) xsinx/[ 1+(cosx)^2] dx +π∫(0->π) (π-x)sinx/[ 1+(cosx)^2] dx
=π^2.∫(0->π) sinx/[ 1+(cosx)^2] dx
=-π^2 [arctan(cosx)]|(0->π)
=π^2 .(π/2)
=(1/2)π^3
I=(1/8)π^3
ie
∫(-π->π) [xsinx.arctan(e^x)]/[ 1+(cosx)^2] dx =(1/8)π^3