分部积分法（在线等！！！）

来源：百度知道 编辑：UC知道 时间：2024/06/23 17:28:53
先祝大家国庆快乐~！！！！
|(lnx)/(x^2)
|ln(x^(1/2))
|arccos(x)
|cos(lnx)
|(x^4)(lnx)^2
|cos(x)ln(sinx)

|(lnx)/(x^2)dx=-|(lnx)d(1/x)
=-lnx/x+|1/xdlnx
=-lnx/x-1/x+c

|ln(x^(1/2))dx
=xln(x^(1/2))-|xdln(x^(1/2)
=xln(x^(1/2))-|x/x^(1/2)*[1/2x^(1/2)]dx
=xln(x^(1/2))-|1/2dx
=xln(x^(1/2))-(1/2)x+c

|arccos(x)dx
cos(lnx) 和上题一样的做法

|(x^4)(lnx)^2dx
=(1/5)|(lnx)^2dx^5
=(1/5)x^5(lnx)^2-(1/5)|x^5 *2lnx *1/xdx
=(1/5)x^5(lnx)^2-(2/5)|x^4*lnxdx
=(1/5)x^5(lnx)^2-(2/25)|lnxdx^5
=(1/5)x^5(lnx)^2-(2/25)x^5*lnx+(2/25)|x^5 *1/xdx
=(1/5)x^5(lnx)^2-(2/25)x^5*lnx+(2/25)|x^4dx
=(1/5)x^5(lnx)^2-(2/25)x^5*lnx+(2/125)x^5+c

|cos(x)ln(sinx)dx
=|ln(sinx)dsinx
=lnsin(x)*sinx-|sinxdlnsin(x)
=lnsin(x)*sinx-|sinx *1/sinx *cosxdx
=lnsin(x)*sinx-|cosxdx
=lnsin(x)*sinx-sinx+c