∫(T-sinT)(1-cosT)2 dT 怎么做?需要详细步骤谢谢...
问题描述：
∫(T-sinT)(1-cosT)2 dT 怎么做?
需要详细步骤
谢谢...
答
∫(T-sinT)(1-cosT)^2dT
=∫T[1-2cost+cos^2(T) ]dT-∫sinT(1-cosT)^ dT
=∫T[1-2cost+(1+cos2T)/2]dT-∫(1-cosT)^2 d(1-cosT)
=3T/2-2∫TdsinT+1/4∫Tdsin2T-(1-cosT)^3/3
=3T/2-(1-cosT)^3/3-2TsinT+2∫sinTdT+Tsin2T/4-1/4∫sin2TdT
=3T/2-(1-cosT)^3/3-2TsinT-2cosT+Tsin2T/4+1/8cos2T+C