`int_0^(pi//4)(sec^2x)/(4+tan x)dx`

Let `u=4+tan\ x`, then `du=sec^2x\ dx`

`int_0^(pi//4)(sec^2x)/(4+tan\ x)dx =[ln\ |4+tan\ x|]_0^(pi//4)`

`=[ln\ |4+tan (pi/4)|]-` `[ln\ |4+tan\ 0|]`

`=ln\ 5-ln\ 4`

`=0.223`