`int(e^(1//x))/(x^(3))dx` का मान ज्ञात कीजिए ।

Explanation

`int(e^(1//x))/(x^(3))dx" माना "(1)/(x)=t`
`=inte^(1//x).(1)/(x).(1)/(x^(2))dx" "rArr" "-(1)/(x^(2))=(dt)/(dx)`
`=inte^(t).t.(-dt)" "rArr" "(1)/(x^(2))dx=-dt`
`=-[t inte^(t)dt-int{(d)/(dt)te^(t)inte^(t)dt}dt]`
`=-[t.e^(t)-inte^(t)dt]`
(t को प्रथम फलन लेने पर)
`=-t.e^(t)+e^(t)+c=e^(t)(1-t)+c`
`=e^(1//x)(1-(1)/(x))+c`