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education/math/MATH1210 (calc 1)/Integrals.md
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@ -6,12 +6,15 @@ An antiderivative is useful when you know the rate of change, and you want to fi
## Examples
> Find the antiderivative of the function $y = x^2$
1. We know that $f'(x) = 2x$
1. We know that $f'(x) = 2x^1$
## Formulas
| Differentiation Formula | Integration Formula |
| ------------------------------ | ------------------------------------------------------- |
| $\dfrac{d}{dx} x^n = nx^{x-1}$ | $\int x^n dx = \dfrac{1}{n+1}x^{n+1}+ C$ for $n \ne -1$ |
| $\dfrac{d}{dx} kx = k$ | $\int k \space dx = kx + C$ |
| Differentiation Formula | Integration Formula |
| ---------------------------------------- | ------------------------------------------------------- |
| $\dfrac{d}{dx} x^n = nx^{x-1}$ | $\int x^n dx = \dfrac{1}{n+1}x^{n+1}+ C$ for $n \ne -1$ |
| $\dfrac{d}{dx} kx = k$ | $\int k \space dx = kx + C$ |
| $\dfrac{d}{dx} \ln \|x\| = \dfrac{1}{x}$ | |
| $\dfrac{d}{dx} e^x = e^x$ | |
| $\dfrac{d]{dx} a^x = \ln$ | |