Evaluate: (i) `int(secxtanx)/(3secx+5)\ dx` (ii) `int(1-cotx)/(1+cotx)\ dx`

Explanation

(i)
`Let {I}=int frac{sec x tan x}{3 sec x+5} d x Putting sec x=t`


`Rightarrow frac{d t}{d x}=sec x tan x `

`Rightarrow d t=sec {x} tan {x} d x `

`therefore I=int frac{d t}{3 t+5} `

`=frac{1}{3} ln |3 t+5|+C `

`=frac{1}{3} ln |3 sec x+5|+C[because, t=sec x]`



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