Compute the integrals: `int_(1/e)^e1/xsin(x-1/x)dx`

Explanation

`I=int_(1//e)^(e)1/x"sin"(x-1/x)dx`
Put `x=1/t,dx=-1/(t^(2))dt`. Thus ,
`I=int_(e)^(1//e)t "sin"(1/t-t)(-1/(t^(2)))dt`
`=int_(e)^(1//e) 1/t "sin"(t-1/t)dt`
`=-int(1//et)^(e)1/t "sin"(t-1/t)dt`
or `I=-I` or `2I=0` or `I=0`