int (e^x(1+x))/(cos^2(xe^x)) dx   সমান -- 

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, \(\int \frac{e^x(1+x)}{\cos^2(xe^x)} dx = \tan(xe^x) + c\) 🥳