计算不定积分∫xcos(x/2)dx 求过程跟答案

题目

计算不定积分∫xcos(x/2)dx 求过程跟答案

答案

∫xcos(x/2)dx
=2∫xcos(x/2)d(x/2)
=2∫xdsin(x/2)
=2xsin(x/2)-2∫sin(x/2)dx
=2xsin(x/2)-4∫sin(x/2)d(x/2)
=2xsin(x/2)+4cos(x/2)+C