你好!
∫[0,+∞](e^-x)sinxdx
= ∫[0,+∞] - sinx de^(-x)
= -sinx e^(-x) |<0,+∞> + ∫[0,+∞] e^(-x) dsinx
= ∫[0,+∞] e^(-x) cosx dx
= ∫[0,+∞] - cosx de^(-x)
= -cosx e^(-x) |<0,+∞> + ∫[0,+∞] e^(-x) dcosx
= 1 - ∫[0,+∞] e^(-x) sinx dx
∴ ∫[0,+∞] e^(-x) sinx dx = 1/2