`tan^(3)2xsec 2x`

Explanation

माना `I=int tan^(3)2x.sec2xdx`
`=int(tan^(2)2x).(tan2x).sec2x dx`
`= int(sec^(2)2x-1).(tan2x.sec2x)dx`
माना `sec2x=t`
`rArr" "2sec 2x. Tan 2x=(dt)/(dx)`
`rArr" "sec 2x. Tan 2x dx=(dt)/(2)`
`I=int(t^(2)-1)(dt)/(2)`
`=(1)/(2)[(t^(3))/(3)-t]+c`
`=(1)/(6)sec^(3)2x-(1)/(2)sec2x+c`