सिद्ध कीजिए कि
`int_(0)^(pi//2)log(tanx)dx=0`

Explanation

`L.H.S.=int_(0)^(pi//2)log(tanx)dx`
`=int_(0)^(pi//2)log((sinx)/(cosx))dx`
`=int_(0)^(pi//2)log(sinx)dx-int_(0)^(pi//2)log(cosx)dx`
`=int_(0)^(pi//2)log(sinx)dx-int_(0)^(pi//2){cos((pi)/(2)-x)}dx`
[प्रगुण (4 ) से ]
`=int_(0)^(pi//2)log(sinx)dx-int_(0)^(pi//2)log(sinx)dx`
= 0 = R.H.S. `" "` यही सिद्ध करना था ।