# How do you evaluate the integral #inte^(-x) dx#?

This integral can be solved by a substitution:

So, now we can substitute:

For simple looking integrands, you should try a quick check to see if substitution works before trying harder integration methods.

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To evaluate the integral ( \int e^{-x} , dx ), use the following steps:

- Recognize that ( \int e^{-x} , dx ) is of the form of the exponential function.
- Apply the integration formula for the exponential function: ( \int e^{ax} , dx = \frac{1}{a} e^{ax} + C ), where ( a ) is a constant and ( C ) is the constant of integration.
- In this case, ( a = -1 ), so ( \int e^{-x} , dx = \frac{1}{-1} e^{-x} + C ).
- Simplify to get ( \int e^{-x} , dx = -e^{-x} + C ).

Thus, the integral of ( e^{-x} ) with respect to ( x ) is ( -e^{-x} + C ), where ( C ) is the constant of integration.

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