intdx/(xsqrt(x^2-1))=f(x)=c হলে, f(x) সমান-

Explanation:

Another Explanation (5): সমাধান: ধরি, \(I = \int \frac{dx}{x\sqrt{x^2-1}}\) এখানে, \(x = \sec\theta\) প্রতিস্থাপন করি। 🥳 তাহলে, \(dx = \sec\theta \tan\theta d\theta\) হবে। সুতরাং, \(I = \int \frac{\sec\theta \tan\theta d\theta}{\sec\theta \sqrt{\sec^2\theta - 1}}\) \(I = \int \frac{\sec\theta \tan\theta d\theta}{\sec\theta \sqrt{\tan^2\theta}}\) \(I = \int \frac{\sec\theta \tan\theta d\theta}{\sec\theta \tan\theta}\) \(I = \int d\theta\) \(I = \theta + c\) যেহেতু \(x = \sec\theta\), সুতরাং \(\theta = \sec^{-1}x\) 🤩 অতএব, \(I = \sec^{-1}x + c\) সুতরাং, \(f(x) = \sec^{-1}x\) 😎