x的5次方除以(x的4次方-2x的3次方+2x-1)不定积分等于多少
答案:2 悬赏:0
解决时间 2021-10-19 10:51
- 提问者网友：杀生予夺
- 2021-10-19 06:10
x的5次方除以(x的4次方-2x的3次方+2x-1)不定积分等于多少
最佳答案
- 二级知识专家网友：傲气稳了全场
- 2021-08-29 09:26
∫x^5dx/(x^4-2x^3+2x-1)
=∫[x+2+(4x^3-2x^2-3x+2)/(x^4-2x^3+2x-1)]dx
= x^2/2+2x+∫(4x^3-2x^2-3x+2)/[(x+1)(x-1)^3]dx
= x^2/2+2x+(1/6)∫[1/(x+1)+23/(x-1)+14/(x-1)^2+2/(x-1)^3]dx
= x^2/2+2x+(1/6)ln|x+1| +(23/6)ln|x-1|-(7/3)/(x-1)-(1/6)/(x-1)^2+C
=∫[x+2+(4x^3-2x^2-3x+2)/(x^4-2x^3+2x-1)]dx
= x^2/2+2x+∫(4x^3-2x^2-3x+2)/[(x+1)(x-1)^3]dx
= x^2/2+2x+(1/6)∫[1/(x+1)+23/(x-1)+14/(x-1)^2+2/(x-1)^3]dx
= x^2/2+2x+(1/6)ln|x+1| +(23/6)ln|x-1|-(7/3)/(x-1)-(1/6)/(x-1)^2+C
全部回答
- 1楼网友：空山清雨
- 2020-11-25 20:00
∫ x/(2x+3)^50 dx
=-(1/98)∫ xd[1/(2x+3)^49]
=-(1/98)[x/(2x+3)^49] + (1/98)∫ dx/(2x+3)^49
=-(1/98)[x/(2x+3)^49] - (1/9048)[1/(2x+3)^48] + c
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