`x(logx)^(2)`

Explanation

माना `I=intx(logx)^(2)dx`
`I=(logx)^(2)int x dx`
`" "-int[(d)/(dx)(logx)^(2)int xdx]dx`
`=(logx)^(2).(x^(2))/(2)-int((2logx)/(x).(x^(2))/(2))dx`
`=(x^(2))/(2)(logx)^(2)-int x log x dx`
`=(x^(2))/(2)(logx)^(2)- [logx int x dx- int{((d)/(dx)logx)int x dx }dx ]+C`
`=(x^(2))/(2)(logx)^(2)-[(x^(2))/(2)logx-int(1)/(x).(x^(2))/(2)]dx+C`
`=(x^(2))/(2)(logx)^(2)-(x^(2))/(2)logx+(1)/(2)int xdx +C`
`=(x^(2))/(2)(logx)^(2)-(x^(2))/(2)logx+(x^(2))/(4)+C`