int(e^x(1+x))/(cos^2(xe^x))dx=?

Explanation:

Another Explanation (5): ```html

সমাধান

ধরি, \(xe^x = z\) অতএব, \(\frac{dz}{dx} = e^x + xe^x = e^x(1+x)\) সুতরাং, \(dz = e^x(1+x)dx\) তাহলে, \(\int \frac{e^x(1+x)}{\cos^2(xe^x)} dx = \int \frac{1}{\cos^2(z)} dz\) আমরা জানি, \(\frac{1}{\cos^2(z)} = \sec^2(z)\) সুতরাং, \(\int \sec^2(z) dz = \tan(z) + c\) z এর মান বসিয়ে পাই, \(\tan(xe^x) + c\) অতএব, \(\int \frac{e^x(1+x)}{\cos^2(xe^x)} dx = \tan(xe^x) + c\) 🎉 ```