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

User SvenK
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1 Answer

6 votes

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)...

User Rawb
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