int(1+1/x)(x+ln x) dx=?

Explanation:

Another Explanation (5): সমাধান: ধরি, \(u = x + \ln x\)। 🧐 তাহলে, \(\frac{du}{dx} = 1 + \frac{1}{x}\) 🤔 সুতরাং, \(du = (1 + \frac{1}{x}) dx\) 🤩 এখন, \(\int (1 + \frac{1}{x}) (x + \ln x) dx = \int u du\) 🤓 আমরা জানি, \(\int u du = \frac{1}{2} u^2 + C\) 😍 অতএব, \(\int (1 + \frac{1}{x}) (x + \ln x) dx = \frac{1}{2} (x + \ln x)^2 + C\) 🥳 সুতরাং, উত্তর: \(\frac{1}{2} (x + \ln x)^2 + C\) 🎉