求不定积分?∫ x sin(x/2) dx - 知识问答

求不定积分?∫ x sin(x/2) dx

3个回答

∫ x sin(x/2) dx
=4∫（x/2)sin(x/2)d(x/2) 令t=x/2
=4∫t sint dt
= -4∫td(cost)
= -4(t cost -∫cost dt)
=4sint - 4t cost+C
=4sin(x/2)-2xcos(x/2)+C

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