Question:
Evaluate the following integrals:
$\int x e^{x^{2}} d x$
Solution:
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 $x^{2}=t$
$\Rightarrow \frac{e^{x^{2}}}{2}+C$
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