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 Q17  Integrate the functions \frac{x }{e^{x^{2}}}

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Given function  \frac{x }{e^{x^{2}}},

Assume the x^2=t

 \therefore 2xdx =dt

\implies \int \frac{x}{e^{x^2}}dx = \frac{1}{2}\int \frac{1}{e^t}dt

= \frac{1}{2}\int e^{-t} dt

= \frac{1}{2}\left ( \frac{e^{-t}}{-1} \right ) +C

= \frac{-1}{2}e^{-x^2} +C

= \frac{-1}{2e^{x^2} }+C, where C is any constant value.

Posted by

Divya Prakash Singh

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