Question

Integral of e^(-xdx? can anyone explain how to evaluate the indefinite integral of e^(-xdx using the substitution rule to do u substitution?

Answer 1

$\displaystyle\int e^{-x}\,\mathrm dx$

You probably know that the antiderivative of $e^x$ is simply $e^x$. So to get something that resembles this form, let $u=-x$. Then $\mathrm du=-\mathrm dx$, or $-\mathrm du=\mathrm dx$.

Now the integral is

$\displaystyle\int e^{-x}\,\mathrm dx=\int e^u(-\mathrm du)=-\int e^u\,\mathrm du=-e^u+C=-e^{-x}+C$