int (e^x(1+x))/(cos^2(xe^x)) dx সমান --
সঠিক উত্তরঃ
B.
tan(xex)+c
Explanation: 
Another Explanation (5):
সমাধান:
ধরি, \(xe^x = z\)
অতএব, \(\frac{d}{dx}(xe^x) = \frac{dz}{dx}\)
\(\implies e^x + xe^x = \frac{dz}{dx}\)
\(\implies e^x(1+x) dx = dz\)
সুতরাং,
\(\int \frac{e^x(1+x)}{\cos^2(xe^x)} dx = \int \frac{dz}{\cos^2(z)}\)
\(= \int \sec^2(z) dz\)
\(= \tan(z) + c\)
\(= \tan(xe^x) + c\)
অতএব, \(\int \frac{e^x(1+x)}{\cos^2(xe^x)} dx = \tan(xe^x) + c\) 🥳
