Question

∫ ex (sec x + tan²x) dx = ? a) eˣsec²x b) eˣsecx c) eˣtan²x d) eˣtanx

Answer 1

None of these options seem to be correct. You can check each result by differentiation:

$(e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)$

$(e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)$

$(e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)$

$(e^x\tan x)'=e^x(\tan x+\sec^2x)$

But none of these are equivalent to $e^x(\sec x+\tan^2x)$...