Explanation:

tan(π/4   -x)  =1- tan x/1+tanx

integration ?^π/4 ₀  2(1-tanx)/(1+tanx) dx 

=?^π/4 ₀     2tan(π/4   -x) 

formula ?₀^a f(x)dx  =f(a-x)dx

= ?^π/4 ₀   2  tan(π/4   -x) 

= ?^π/4 ₀   2  tan(π/4 –π/4 +x)

= ?^π/4 ₀    2 tan x

=2[log sec x]₀^π/4

=2log sec π/4  -log sec (0)

=2log √2 -0

=2 log √2

=  log 2