indefinite integrals

Question

The integral ∫eˣ dx equals

RankGuru · Accepted Answer

1. **Unique Property**: The natural exponential function $f(x) = e^x$ is the only function (aside from zero) that acts as its own derivative and its own integral.
2. **Relation**: Since $\frac{d}{dx} e^x = e^x$, the family of antiderivatives is $e^x + C$.
3. **Result**: $\int e^x \, dx = e^x + C$.

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indefinite integrals

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indefinite integrals

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