int dx/(e^x +e^-x) =? 

Explanation:

Another Explanation (5): সমাধান: \[ \int \frac{dx}{e^x + e^{-x}} \] আমরা লিখতে পারি, \[ \int \frac{dx}{e^x + \frac{1}{e^x}} = \int \frac{e^x}{e^{2x} + 1} dx \] ধরি, \(e^x = t\), সুতরাং \(e^x dx = dt\). তাহলে, \[ \int \frac{dt}{t^2 + 1} = \tan^{-1}(t) + c \] যেহেতু \(t = e^x\), \[ \int \frac{dx}{e^x + e^{-x}} = \tan^{-1}(e^x) + c \] সুতরাং, উত্তর: \(\tan^{-1}(e^x) + c\) 🎉