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`