Explanation: 
Another Explanation (5):
সমাধান:
ধরি, \(u = 1 + e^x\)
তাহলে, \(\frac{du}{dx} = e^x\) অথবা, \(du = e^x dx\)
এখন, যখন \(x = 0\), তখন \(u = 1 + e^0 = 1 + 1 = 2\)
এবং যখন \(x = \ln 2\), তখন \(u = 1 + e^{\ln 2} = 1 + 2 = 3\)
সুতরাং,
\(\int_0^{\ln 2} \frac{e^x}{1 + e^x} dx = \int_2^3 \frac{1}{u} du\)
\(= [\ln |u|]_2^3\)
\(= \ln |3| - \ln |2|\)
\(= \ln 3 - \ln 2\)
\(= \ln \frac{3}{2}\) 🥳
অতএব, \(\int_0^{\ln 2} \frac{e^x}{1 + e^x} dx = \ln \frac{3}{2}\) 🤩
