`int_(e)^(e^(2)) {1/logx-1/((log x)^(2))}dx` का मान ज्ञात कीजिएः

Explanation

`I=underset(e)overset(e^(2))int {1/logx-1/((log x)^(2))}dx`
`=underset(e)overset(e^(2))int 1/log xdx- underset(e)overset(e^(2))int (1)/((log x)^(2))dx`
`=[(1)/logx.x]_(e)^(e^(2))-underset(e)overset(e^(2))int {-1/((log x)^(2)).1/x.x}dx-underset(e)overset(e^(2))int (1)/((log x)^(2))dx`
`=[(x)/(log x)]_(e)^(e^(2))+underset(e)overset(e^(2))int (1)/((logx)^(2))dx`
`=((e^(2))/(log e^2)-e/(log e))=(e^(2))/(2log e)-(e)/(log e.)=(e^(2))/(2)=e`