Mathematics

Evaluate:$$\displaystyle\int{\ln{\left(\dfrac{1}{{e}^{x}}\right)}dx}$$


SOLUTION
$$\displaystyle\int{\ln{\left(\dfrac{1}{{e}^{x}}\right)}dx}$$
$$=\displaystyle\int{\ln{\left({e}^{-x}\right)}dx}$$
$$=\displaystyle\int{-x\ln{e}dx}$$
$$=-\displaystyle\int{x\,dx}$$
$$=\dfrac{-{x}^{2}}{2}+c$$ where $$c$$ is the constant of integration.

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Subjective Medium Published on 17th 09, 2020
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