计算不定积分∫xcos(x/2)dx 求过程跟答案_数学解答

计算不定积分∫xcos(x/2)dx 求过程跟答案

人气：278 ℃　时间：2020-06-27 08:47:05

解答

∫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