What is the antiderivative of #x sin (x/2)#?

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Answer 1 · 2018-05-17T23:48:43

#int xsin(x/2)dx =-2xcos(x/2) + 4sin(x/2)+C#

Evaluate the indefinite integral:

#int xsin(x/2)dx#

by parts:

#int xsin(x/2)dx = int x d/dx (-2cos(x/2))dx#

#int xsin(x/2)dx =-2xcos(x/2) + 2 int cos(x/2)dx#

#int xsin(x/2)dx =-2xcos(x/2) + 4 int cos(x/2)d(x/2)#

#int xsin(x/2)dx =-2xcos(x/2) + 4sin(x/2)+C#