在线等 跪求不定积分 有答案马上采纳 急~~~~~~~~ 财富不多，已经全给了。 求大侠帮解答一下~~非常感谢

发布网友 发布时间：2022-04-23 12:21

我来回答

共3个回答

热心网友 时间：2023-10-13 04:50

∫ sin(3x - 2)cos²(7x - 1) dx
= ∫ sin(3x - 2)cos(7x - 1) * cos(7x - 1) dx
= ∫ (1/2)[sin(3x - 2 + 7x - 1) + sin(3x - 2 - 7x + 1)] * cos(7x - 1) dx
= ∫ (1/2)sin(10x - 3)cos(7x - 1) - (1/2)sin(4x + 1)cos(7x - 1) dx
= ∫ (1/4)[sin(17x - 4) + sin(3x - 2)] dx - ∫ (1/4)[sin(11x) + sin(- 3x + 2)] dx
= (1/4)∫ sin(17x - 4) dx - (1/4)∫ sin(11x) dx + (1/2)∫ sin(3x - 2) dx
= - (1/4)(1/17)cos(17x - 4) + (1/4)(1/11)cos(11x) - (1/2)(1/3)cos(3x - 2) + C
= (1/44)cos(11x) - (1/68)cos(17x - 4) - (1/6)cos(3x - 2) + C
——————————————————————————————————————————
∫ cos⁵x/√(sin³x) dx
= ∫ (1 - cos²x)²/√(sin³x) d(sinx)
= ∫ (1 - t²)²/t^(3/2) dt，t = sinx
= ∫ (1 - 2t² + t⁴)/t^(3/2) dt
= ∫ t^(-3/2) dt - 2∫ √t dt + ∫ t^(5/2) dt
= -2/√t - (4/3)t^(3/2) + (2/7)t^(7/2) + C
= -2/√sinx - (4/3)(sinx)^(3/2) + (2/7)(sinx)^(7/2) + C
= 2(3sin⁴x - 14sin²x - 21)/(21√sinx) + C
——————————————————————————————————————————
∫ cos⁵x/cos²x dx
= ∫ cos³x dx
= ∫ (1 - sin²x) d(sinx)
= sinx - (1/3)sin³x + C
——————————————————————————————————————————
∫ sin⁴(tanx)/cos²x dx
= ∫ sin⁴(tanx) * sec²x dx
= ∫ sin⁴(tanx) d(tanx)
= ∫ sin⁴z dz，z = tanx
= ∫ (cos²x)² dz
= ∫ [(1 - cos2z)/2]² dz
= (1/4)∫ (1 - 2cos2z + cos²2z) dz
= (1/4)∫ (1 - 2cos2z) dz + (1/4)(1/2)∫ (1 + cos4z) dz
= (1/4)(z - sin2z) + (1/8)(z + 1/4 * sin4z) + C
= (3/8)tanx - (1/4)sin(2tanx) + (1/32)sin(4tanx) + C
——————————————————————————————————————————
∫ arcsin(3x - 2) dx
= (1/3)∫ arcsin(3x - 2) d(3x - 2)
= (1/3)∫ arcsinz dz，z = 3x - 2
= (z/3)arcsinz - (1/3)∫ z d(arcsinz)
= (z/3)arcsinz - (1/3)∫ z/√(1 - z²) dz
= (z/3)arcsinz - (1/3)(-1/2)∫ d(1 - z²)/√(1 - z²)
= (z/3)arcsinz + (1/6) · 2√(1 - z²) + C
= (3x - 2)/3 * arcsin(3x - 2) + (1/3)√[1 - (3x - 2)²] + C
= (1/3)(3x - 2)arcsin(3x - 2) + (1/3)√(12x - 3 - 9x²) + C

热心网友 时间：2023-10-13 04:50

老了！这些都不会了！我的天呀！

热心网友 时间：2023-10-13 04:51

看不懂，不好意思帮不了你