计算∫xcosx/3dx；数学基础差,注：课本上的答案为3xsinx/3+9cosx/3+c；谢谢

Question

计算∫xcosx/3dx；数学基础差,注：课本上的答案为3xsinx/3+9cosx/3+c；谢谢

Answer 1

分部积分法：
∫xcos(x/3)dx
=3∫xdsin(x/3)
=3[xsin(x/3)-∫sin(x/3)dx]
=3[xsin(x/3)-3∫sin(x/3)d(x/3)]
=3xsin(x/3)+9cos(x/3)+C