Evaluate: `int(secxtanx)/(3secx+5)dx`

Explanation

`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`]