Question

What's the integral of `int 1/(secx+tanx)dx`?

Answer 1

`int 1/(sec x+tan x)d x=l n(1+sin x) + C`

Explanation:

`int 1/(sec x+tan x)d x=(d x)/(1/cos x+sin x/cos x)`
`int (cos x d x)/(1+sin x)" "1+sin x=u" "cos x d x=d u`
`int (d u)/u`
`int 1/(sec x+tan x)d x=l n u +C`
`int 1/(sec x+tan x)d x=l n(1+sin x) + C`