The correct option is B 14(sec x+tan x)4[12+13(sec x+tan x)2]+c
Put t=sec x+tan x⇒dtt=sec x dx
∫sec2 x(sec x+tan x)5 dx=∫12(t+1/t)t5dtt=12∫(t−5+t−7) dt=12[t−4−4+t−6−6]+c=−12[14(sec x+tan x)4+16(sec x+tan x)6]+c=−14(sec x+tan x)4[12+13(sec x+tan x)2]+c