Question

\[\  ∫    x   \text{ e}^{x^2} dx\]

Answer 1

\[\int x . e^{x^2} dx\]
\[\text{Let x}^2 = t\]
\[ \Rightarrow \text{2x dx} = dt\]
\[ \Rightarrow \text{x dx} = \frac{dt}{2}\]
\[Now, \int x . e^{x^2} dx\]
\[ = \frac{1}{2}\int e^t dt\]
\[ = \frac{1}{2} e^t + C\]
\[ = \frac{1}{2} e^{x^2} + C\]