Solve ∫ e^x dx

Step-by-step solution

1. The exponential function $e^x$ is its own derivative — and its own antiderivative.

2. Verify: $\frac{d}{dx}(e^x + C) = e^x$.

3. Therefore $\int e^x \, dx = e^x + C$.

4. This makes $e^x$ unique among elementary functions — it's the unique fixed point of differentiation up to constants.