∫1+tanxtan(x+a)dx

We know that, tan(c-b) = (tan c – tan b)/(1+tan c * tan b),
So, (1+tan c * tan b) = (tan c – tan b) / tan (c-b),
Put c= x+a, b=x,
(1+tanx * tan(x+a)) = (tan(x+a) – tan x) / tan(x+a-x) = (tan(x+a) – tan x) / tan a,
Now , seperate the two terms in 2 diff integrals and solve.
ATB