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$\int e^{- x} (1 - \tan x) \sec x d x is equal to$

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e−xsec⁡x+c

e−xtan⁡x+c

−e−xtan⁡x+c

−e−xsec⁡x+c

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detailed solution

Correct option is D

Putting x=−z, we get I=∫−ez(sec⁡z+sec⁡z⋅tan⁡z)dz=−∫ezsec⁡z+ddz(sec⁡z)dz=−ezsec⁡z+k∴ I=−e−xsec⁡x+k

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∫e−x(1−tan⁡x)sec⁡xdx is equal to

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$\int e^{- x} (1 - \tan x) \sec x d x is equal to$