inte^x(tanx-lncosx)dx =কত?
সঠিক উত্তরঃ
C.
ex ln|secx| + c
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, \( \int e^x (\tan x - \ln \cos x) dx = e^x \ln |\sec x| + c \) 🤩🤩🤩
