int e^x(tanx+logsecx)dx=? 

Explanation:

Another Explanation (5): সমাধান: আমরা জানি, \( \int e^x [f(x) + f'(x)] dx = e^x f(x) + c \)। এখানে, \( f(x) = \log(\sec x) \) হলে, \( f'(x) = \frac{d}{dx} \log(\sec x) = \frac{1}{\sec x} \cdot \frac{d}{dx} (\sec x) \) \( = \frac{1}{\sec x} \cdot \sec x \tan x = \tan x \) সুতরাং, \( \int e^x (\tan x + \log \sec x) dx = \int e^x (\log \sec x + \tan x) dx \) এখানে, \( f(x) = \log \sec x \) এবং \( f'(x) = \tan x \)। অতএব, \( \int e^x (\tan x + \log \sec x) dx = e^x \log \sec x + c \) 🥳 সুতরাং, উত্তর: \( e^x \log \sec x + c \) 🤩