Question

分部积分法求怎么求

Answer 1

I = ∫e^(-x)cosxdx = ∫e^(-x)dsinx

= e^(-x)sinx - ∫-e^(-x)sinxdx

= e^(-x)sinx - ∫e^(-x)dcosx

= e^(-x)sinx - e^(-x)cosx -∫e^(-x)cosxdx

= e^(-x)(sinx-cosx) - I

2I = e^(-x)(sinx-cosx)

I = (1/2)e^(-x)(sinx-cosx)+C