Solution. We want to determine the integral of e^{-x}, i.e.:
\begin{align*}
\int \frac{1}{e^x} dx = \int e^{-x}dx.
\end{align*}\begin{align*}
\int e^{-x} dx &= - \int e^u du \\
&= -e^u + C \\
&= -e^{-x} + C.
\end{align*}
integral of inverse e^x
What is the integral of inverse e^x?
The integral of e^{-x} is -e^{-x} + C.
Solution. We want to determine the integral of e^{-x}, i.e.:
We will use the substitution method: let u = -x, then du = -dx. Then we get the following integral:
Therefore, the integral of e^{-x} is -e^{-x} + C.
Solution. We want to determine the integral of e^{-x}, i.e.:
