`int_(1)^(2) (log x)/(x^(2))dx` का मान ज्ञात कीजिएः।

Explanation

यहाँ `I=underset(1)overset(2)int (log x)/(x^(2))dx `
`=underset(1)overset(2)int underset(I)(log)x. 1/x^(2)dx`
`=[logx.(-1/x)]_(1)^(2)-underset(1)overset(2)int 1/x.(-1/x)dx`
`=[-(log x)/(x)]_(1)^(2)+underset(1)overset(2)int (1)/(x^(2))dx`
`=[-(log x)/(x)]_(1)^(2)+[-1/x]_(1)^(2)`
`=[-1/2log2+logq]+[-1/2+1]`
`=-1/2log 2+0+1/2=1/2(-log2+1)`
`=1/2(-log2+log e)=1/2 log (e/2)`