Evaluate: (i) `inttan^5xsec^4x\ dx` (ii) `intsec^6xtanx\ dx`

Explanation

(i)
`int tan ^{5} x sec ^{4} x d x `

`=int tan ^{5} x cdot sec ^{2} x cdot sec ^{2} x d x `

`=int tan ^{5} x(1+tan ^{2} x) sec ^{2} x d x `

`text { Let } tan x=t `

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

`text { Now } int tan ^{5} x(1+tan ^{2} x) sec ^{2} x d x `

`=int t^{5}(1+t^{2}) d t `

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