Evaluate: (i) `inttan^3xsec^2x\ dx` (ii) `inttanxsec^4x\ dx`

Explanation

(i)

`text { Let } I=int tan ^{3} x cdot sec ^{2} x d x `

`text { Let } tan x=t `

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

`therefore int t^{3} cdot d t `

`=frac{t^{4}}{4}+C `

`=frac{tan ^{4} x}{4}+C(because t=tan x)`


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