Evaluate: `inttan^4x dx`

Explanation

`text { Let } I=int tan ^{4} x d x`

`=int tan ^{2} x cdot tan ^{2} x d x`

`=int(sec ^{2} x-1) tan ^{2} x d x`

`=int sec ^{2} x cdot tan ^{2} xdx-int tan ^{2} xdx`

`=int tan ^{2} x cdot sec ^{2} x-int(sec ^{2} x-1) d x`

`text { Putting } tan x=t text { in the Ist integral }`

`Rightarrow sec ^{2} x d x=d t`

`therefore I=int t^{2} cdot d t-int(sec ^{2} x-1) d x`

...