哪位老兄知道用分部积分法求解∫e∧(R/L)tsinωtdt的详细步骤

Question

哪位老兄知道用分部积分法求解∫e∧(R/L)tsinωtdt的详细步骤

Answer 1

∫e^(R/L)tsinwtdt
=(-1/w)∫e^(R/L)tdcoswt
=(-1/w)e^(R/L)t coswt +(1/w)∫coswtde^(R/L)t
=(-1/w)e^(R/L)t coswt +(R/Lw^2)∫e^(R/L)tdsinwt
=(-1/w)e^(R/L)t coswt +(R/Lw^2)e^(R/L)t sinwt -(R/Lw)^2)∫e^(R/L)twinwtdt
(1+(R/Lw)^2) ∫e^(R/L)t sinwtdt =(-1/w)e^(R/L)t coswt +(R/Lw^2)e^(R/L)t sinwt