Evaluate: (i) `inttanxsec^2x\ sqrt(1-tan^2x)\ dx` (ii) `intlogx\ (sin{1+(logx)^2})/x\ dx`

Explanation

(i)

`int tan x cdot sec ^{2} x sqrt{1-tan ^{2} x} d x `

`text { Let } tan x=t `

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

`text { Now, } int tan x cdot sec ^{2} x sqrt{1-tan ^{2} x} d x `

`=int t cdot sqrt{1-t^{2}} d t `

`text { Again let } t^{2}=p `

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