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

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a

excos⁡x+C

b

exsec⁡x+C

c

exsin⁡x+C

d

extan⁡x+C

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detailed solution

Correct option is B

Let I=∫exsec⁡x(1+tan⁡x)dx⇒I=∫exsec⁡xdx+∫exsec⁡xtan⁡xdx -----iNow ∫exsec⁡xdx=sec⁡x∫exdx−∫ddxsec⁡x∫exdxdx=exsec⁡x−∫sec⁡xtan⁡xexdx ----ii On putting the value from Eq. (ii)inEq. (i),we get I=exsec⁡x−∫exsec⁡xtan⁡xdx+∫sec⁡xtan⁡xexdx+C⇒I=exsec⁡x+C

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