亲,请求此二不定积分: ∫cos2(2x+1)·dx;∫cos3x·dx.

2025-03-03 05:34:59
推荐回答(1个)
回答1:

∫ cos²(2x + 1) dx
= (1/2)∫ [1 + cos(2(2x + 1))] dx
= (1/2)∫ dx + (1/2)(1/4)∫ cos(4x + 2) d(4x + 2)
= x/2 + (1/8)sin(4x + 2) + C

∫ cos³x dx
= ∫ cos²x dsinx
= ∫ (1 - sin²x) dsinx
= sinx - (1/3)sin³x + C