`sec^(6)x`

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`"Let I"=int sec^(6)xdx=int sec^(4)x sec^(2)x dx`
`=int (sec^(2)x)^(2)sec^(2)xdx`
`=int(1+tan^(2)x)sec^(2)xdx`
Put tan x=t. Then `sec^(2)xdx=dt`
`therefore I=f(1+t^(2))^(2)dt`
`=int(1+2t^(2)+t^(4))dt`
`=int 1 dt+2 intt^(2)dt+intt^(4)dt`
`=t+2. (t^(3))/(3)+(t^(5))/(5)+c`
`=tan x+(2)/(3)tan^(3)x+(1)/(5)tan^(5)x+c`
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