Question:
$\frac{x}{e^{x^{2}}}$
Solution:
Let $x^{2}=t$
$\therefore 2 x d x=d t$
$\Rightarrow \int \frac{x}{e^{x^{2}}} d x=\frac{1}{2} \int \frac{1}{e^{t}} d t$
$=\frac{1}{2} \int e^{-t} d t$
$=\frac{1}{2}\left(\frac{e^{-t}}{-1}\right)+\mathrm{C}$
$=-\frac{1}{2} e^{-x^{2}}+\mathrm{C}$
$=\frac{-1}{2 e^{x^{2}}}+\mathrm{C}$
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