`(1)/(e^(x)-1)" "` [ संकेत: `e^(x)=t` रखिए ]

Explanation

`int(1)/(x^(x)-1)dx=int(e^(x))/(e^(x)(e^(x)-1))dx`
`=int(1)/(t(t-1))dt=int((1)/(t-1)-(1)/(t))dt" माना "e^(x)=t`
`=log|t-1|-logt+c=log|(t-1)/(t)|+c" "rArr e^(x)dx=dt`
`=log|(e^(x)-1)/(e^(x))|+c=log|1-e^(-x)|+c`