Integrate the function: x e^ x^ 2 - Vidyadip

Question

Integrate the function: $\frac{x}{e^{x^{2}}}$

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Answer

Let x² = t
$\Rightarrow$ 2xdx = dt
$\Rightarrow \int \frac{x}{e^{x^{2}}} d x=\frac{1}{2} \int \frac{1}{e^{t}} d t$
$=\frac{1}{2} \int e^{-t} d t$
$= \frac{1}{2}\left(\frac{e^{-t}}{-1}\right)+C$
$= \frac{-1}{2} e^{-x^{2}}+C$
$= \frac{-1}{2 e^{x^{2}}}+C$

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