Explanation: 
Another Explanation (5):
সমাধান:
ধরি, \(I = \int_0^1 xe^{x^2} dx\)
এখানে, \(x^2 = z\) ধরলে,
\(2x dx = dz\)
সুতরাং, \(x dx = \frac{1}{2} dz\)
যখন \(x = 0\), তখন \(z = 0^2 = 0\)
এবং যখন \(x = 1\), তখন \(z = 1^2 = 1\)
অতএব,
\(I = \int_0^1 e^z \frac{1}{2} dz\)
\(I = \frac{1}{2} \int_0^1 e^z dz\)
\(I = \frac{1}{2} [e^z]_0^1\)
\(I = \frac{1}{2} [e^1 - e^0]\)
\(I = \frac{1}{2} [e - 1]\)
সুতরাং, \(\int_0^1 xe^{x^2} dx = \frac{1}{2}(e-1)\) 🥳
