Mathematics

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


SOLUTION
Put $$x^2=t$$
$$\therefore 2xdx=dt$$
$$\Rightarrow\displaystyle  \int \frac {x}{e^{x^2}}dx=\frac {1}{2}\int \frac {1}{e^t}dt$$
$$\displaystyle =\frac {1}{2}\int e^{-t}dt$$
$$\displaystyle =\frac {1}{2}\left (\frac {e^{-t}}{-1}\right )+C$$
$$\displaystyle =-\frac {1}{2}e^{-x^2}+C$$
$$\displaystyle =\frac {-1}{2e^{x^2}}+C$$
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Subjective Medium Published on 17th 09, 2020
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