Evaluate: (i) `intsecxlog(secx+tanx)\ dx` (ii) `intcos e c\ xlog(cos e c\ x-cotx)\ dx`

Explanation

(i) `I=intsecxlog(secx+tanx)\ dx`
Let `t=log(secx+tanx)`
`=>secx dx=dt`
so, `I=int tdt`
`=t^2/2+c`
`={log(secx+tanx)}^2/2+c`


(ii) `I=intcos e c\ xlog(cos e c\ x-cotx)\ dx`
Let `t=log(cosec x-cotx)`
`=>(-cosecx * cotx+cosec^2x)/(cosecx-cotx)dx=dt`
`=>cosecx dx=dt`
so,`I=int tdt`
`=t^2/2+c`
`={log(cosec x-cotx)}^2/2+c`