inte^x(tanx-lncosx)dx =কত?

Explanation:

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