(LNX/X2)2的不定积分
1个回答
展开全部
∫(lnx/x^2)^2dx
=∫[(lnx)^2]/x^4dx
=∫[(lnx)^2]d{-(1/3)x^(-3)}
=-(1/3)x^(-3)[(lnx)^2]+∫(1/3)x^(-3)[2(lnx)(1/x)]dx
=-(1/3)x^(-3)[(lnx)^2]+(2/3)∫x^(-4)lnxdx
=-(1/3)x^(-3)[(lnx)^2]+(2/3)∫lnxd{-(1/3)x^(-3)}
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx+(2/3)∫(1/3)x^(-3)(1/x)dx
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx+(2/9)∫x^(-4)dx
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx-(2/27)x^(-3)+C
如果有不妥之处请回复.
=∫[(lnx)^2]/x^4dx
=∫[(lnx)^2]d{-(1/3)x^(-3)}
=-(1/3)x^(-3)[(lnx)^2]+∫(1/3)x^(-3)[2(lnx)(1/x)]dx
=-(1/3)x^(-3)[(lnx)^2]+(2/3)∫x^(-4)lnxdx
=-(1/3)x^(-3)[(lnx)^2]+(2/3)∫lnxd{-(1/3)x^(-3)}
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx+(2/3)∫(1/3)x^(-3)(1/x)dx
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx+(2/9)∫x^(-4)dx
=-(1/3)x^(-3)[(lnx)^2]-(2/9)x^(-3)lnx-(2/27)x^(-3)+C
如果有不妥之处请回复.
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
