求cosxcosx/2dx的积分答案应该是2(sinx/2-2/3sinx^3x/2)+c

Question

求cosxcosx/2dx的积分
答案应该是2(sinx/2-2/3sinx^3x/2)+c

Answer 1

原式=∫ （cos^2 X/2- sin^2 x/2）cos x/2 dx =2∫ (cos^2 x/2- sin^2 x/2)d sin x/2
= 2∫ (1-2sin^2 x/2) d sin x/2
=2sinx/2-3/4sin^2 x/2+C