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

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etan⁡x⋅cos⁡x+C

etan⁡x⋅sin⁡x+C

−etan⁡x⋅cos⁡x+C

etan⁡x⋅sec⁡x+C

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detailed solution

Correct option is C

I=∫etan⁡x(sinx-secx)dx=∫sin⁡x⋅etan⁡xdx−∫sec⁡x⋅etan⁡xdx=−etan⁡x⋅cos⁡x+∫cos⁡x⋅etan⁡x⋅sec2⁡xdx−∫sec⁡x⋅etan⁡xdx=−cos⁡x⋅etan⁡x+C

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∫etan⁡x(sin⁡x−sec⁡x)dx, is equal to

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