`intsec^(4)xtanxdx=?`

Explanation

`intsec^(4)xtanxdx=intsec^(2)*sec^(2)xtanxdx`
`=int(1+tan^(2)x)sec^(2)xtanxdx`
`=int(1+t^(2))tdt," where "tanx=t`
`=inttdt+intt^(3)dt=(t^(2))/(2)+(t^(4))/(4)+C`
`=(1)/(2)tan^(2)x+(1)/(4)tan^(4)x+C`.