Evaluate: (i) `intsqrt(tanx)sec^4x\ dx`

Explanation

`(i)I=∫sqrt(tanx)​sec^4xdx`

`I=∫sqrt(tanx)​sec^2xsec^2xdx`

`I=∫sqrt(tanx)(1+tan^2x)sec^2xdx`

`I=∫sqrt(tanx)​sec^2xdx+∫sqrt(tanx)tan^2xsec^2xdx`


`I=∫sqrt(tanx)
​sec^2xdx+∫(tanx)^(1/2​+2)sec^2xdx`

`I=∫sqrt(tanx)
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