`inttan^5theta sec^4theta d theta`

Explanation

`inttan^5theta sec^4theta d theta`
=`inttan^5theta.(1+tan^2theta).sec^2thetad theta`
[Put `tantheta=1`
Then `sec^2thetad theta=dt`]
=`intt^5.(1+t^2).dt=int(t^5+t^7)dt`
=`1/6t^6+1/8t^8+C=1/6tan^6theta+1/8tan^8theta+C`