Question

xsinx/2dx求不定积分

Answer 1

本题不定积分计算过程如下：
∫xsinx/2dx
=∫xsinx/2d(x/2)
=-∫xd(cosx/2)
=-xcosx/2+∫cosx/2dx
=-xcosx/2+2∫cosx/2d(x/2)
=-xcosx/2+2sinx/2+c.

Answer 2

∫xsin(x/2)dx
=(-2)*∫xd[cos(x/2)]
=(-2x)*cos(x/2)+2*∫cos(x/2)dx
=(-2x)*cos(x/2)+4*sin(x/2)+C，其中C是任意常数