Evaluate

in this integral we will use the formula 1+tan2x=sec2x,


I = ∫sec2x sec4x dx


= ∫sec2x (1 + tan2x)2 dx


Now put tan x=t which means sec2xdx=dt,


I = ∫(1+t2)2 dt


= ∫(1+t4+2t2) dt


Now put the value of t, which is t=tan x in above integral-



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