what is the intrigation value of tanx/(tan(x)^2+tan(x)+1)

Dear Chandan
multiply by tan x in numerator and denominator
tan²x / [(tan x) * (tan² x + tan x +1)]
= sec² x – 1 / [(tan x) * (tan² x + tan x +1)]
now put tanx = t
sec² x * dx = dt
now, it becomes
[dt / t (t² + t +1) ]– dx/ tanx (tan² x +tan x +1)
now you can solve it
Regards
Arun (askIITians forum expert)