Integral of e⁻ˣ

Differentiate it: the derivative of -e^{-x} is e^{-x}. CalcViz checks every antiderivative this way before showing it.

\int e^{-x}\,dx = -e^{-x} + C

Reverse chain rule: divide by the inner slope −1. The area from 0 to ∞ is exactly 1.

Exponential rule
∫eᵘ du = eᵘ. Divide by the inner slope -1 (reverse chain rule).
$\int e^{-x}\,dx = -e^{-x}$

Constant C = 0.0

Every choice of C gives a valid antiderivative, since shifting up or down doesn’t change the slope.

Questions students ask

What is the integral of e⁻ˣ?

$\int e^{-x}\,dx = -e^{-x} + C$ .

How do you integrate e⁻ˣ?

Reverse chain rule: divide by the inner slope −1. The area from 0 to ∞ is exactly 1.

How can I check the answer?

Differentiate it: the derivative of $-e^{-x}$ is $e^{-x}$ . CalcViz checks every antiderivative this way before showing it.