int(dθ)/(tanθlogsinθ)=? 

Explanation:

Another Explanation (5): সমাধান: ধরি, \(I = \int \frac{d\theta}{\tan\theta \cdot \log(\sin\theta)}\) আমরা জানি, \(\tan\theta = \frac{\sin\theta}{\cos\theta}\) সুতরাং, \(I = \int \frac{\cos\theta \, d\theta}{\sin\theta \cdot \log(\sin\theta)}\) এখন, ধরি, \(u = \log(\sin\theta)\) তাহলে, \(\frac{du}{d\theta} = \frac{1}{\sin\theta} \cdot \cos\theta = \frac{\cos\theta}{\sin\theta}\) সুতরাং, \(du = \frac{\cos\theta}{\sin\theta} \, d\theta\) তাহলে, \(I = \int \frac{du}{u}\) আমরা জানি, \(\int \frac{1}{x} dx = \log|x| + C\) সুতরাং, \(I = \log|u| + C\) \(u\) এর মান বসিয়ে পাই, \(I = \log|\log(\sin\theta)| + C\) সুতরাং, \(\int \frac{d\theta}{\tan\theta \cdot \log(\sin\theta)} = \log(\log(\sin\theta)) + C\) 🥳🎉 অতএব, উত্তর: \( \log(\log(\sin\theta)) + C \)✅