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Prove

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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