用分部积分法求∫(e~e^2)xln^2xdx
答案:2 悬赏:70
解决时间 2021-02-01 16:32
- 提问者网友：江山如画
- 2021-02-01 08:20
用分部积分法求∫(e~e^2)xln^2xdx
最佳答案
- 二级知识专家网友：社会水太深
- 2021-02-01 09:55
∫xln^2xdx
=1/2 *∫ln^2xdx^2
=1/2 *ln^2x *x^2 -∫1/2 *x^2 dln^2x
=1/2 *ln^2x *x^2 -∫1/2 *x *2lnx dx
=1/2 *ln^2x *x^2 -1/2 ∫lnx d(x^2)
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +∫1/2 x^2 d(lnx)
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +∫1/2 x dx
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +1/4 x^2
代入上下限e^2和e
=2e^4 -e^4+1/4 e^4 -1/2e^2 +1/2e^2 -1/4e^2
=5/4 e^4 -1/4e^2
=1/2 *∫ln^2xdx^2
=1/2 *ln^2x *x^2 -∫1/2 *x^2 dln^2x
=1/2 *ln^2x *x^2 -∫1/2 *x *2lnx dx
=1/2 *ln^2x *x^2 -1/2 ∫lnx d(x^2)
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +∫1/2 x^2 d(lnx)
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +∫1/2 x dx
=1/2 *ln^2x *x^2 -1/2 * lnx *x^2 +1/4 x^2
代入上下限e^2和e
=2e^4 -e^4+1/4 e^4 -1/2e^2 +1/2e^2 -1/4e^2
=5/4 e^4 -1/4e^2
全部回答
- 1楼网友：余生继续浪
- 2021-02-01 10:31
我不会~~~但还是要微笑~~~：）
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