Evaluate the following integrals:

Assume $x^{2}=t$

$\Rightarrow 2 x \cdot d x=d t$

$\Rightarrow x \cdot d x=\frac{d t}{2}$

Substituting $\mathrm{t}$ and $\mathrm{dt}$

$\Rightarrow \int e^{t} \cdot \frac{d t}{2}$

$\Rightarrow \frac{1}{2} e^{t}+c$

But $x^{2}=t$

$\Rightarrow \frac{e^{x^{2}}}{2}+C$