Evaluate the integral int e^x secx (1+tanx)dx -

A. e^-xcosx + c

B. e^xsec2x + c

C. e^xsecx + c

D. e^xsinx + c

সঠিক উত্তরঃ C. e^xsecx + c

Explanation:

Another Explanation (5): ```html

সমাধান:

ধরি, \(I = \int e^x \sec x (1 + \tan x) dx\)

আমরা জানি, \(\int e^x [f(x) + f'(x)] dx = e^x f(x) + c\)

এখানে, \(f(x) = \sec x\) হলে, \(f'(x) = \sec x \tan x\)

তাহলে, \(I = \int e^x (\sec x + \sec x \tan x) dx\)

\(= \int e^x [\sec x + \frac{d}{dx}(\sec x)] dx\)

সুতরাং, \(I = e^x \sec x + c\) 🥳

অতএব, \(\int e^x \sec x (1 + \tan x) dx = e^x \sec x + c\) 😎

উত্তর: \(e^x \sec x + c\) 🎉

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