int (e^(5x)+e^(3x))/(e^x+e^-x) dx এর মান হলো __ 

Explanation:

Another Explanation (5): সমাধান: ধরি, \(I = \int \frac{e^{5x} + e^{3x}}{e^x + e^{-x}} dx\) \(I = \int \frac{e^{3x}(e^{2x} + 1)}{e^x + \frac{1}{e^x}} dx\) \(I = \int \frac{e^{3x}(e^{2x} + 1)}{\frac{e^{2x} + 1}{e^x}} dx\) \(I = \int e^{3x} \cdot e^x dx\) \(I = \int e^{4x} dx\) আমরা জানি, \(\int e^{ax} dx = \frac{e^{ax}}{a} + c\) অতএব, \(I = \frac{e^{4x}}{4} + c\) \(I = \frac{1}{4} e^{4x} + c\) 😍 সুতরাং, \(\int \frac{e^{5x} + e^{3x}}{e^x + e^{-x}} dx = \frac{1}{4} e^{4x} + c\) 🎉