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education/math/MATH1210 (calc 1)/Integrals.md
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@ -18,11 +18,11 @@ An antiderivative is useful when you know the rate of change, and you want to fi
| $\dfrac{d}{dx} \ln \|x\| = \dfrac{1}{x}$ | <br>$\int \dfrac{1}{x}dx = \ln \|x\| + C$ |
| $\dfrac{d}{dx} e^x = e^x$ | <br>$\int e^x dx = e^x + C$ |
| $\dfrac{d}{dx} a^x = (\ln{a}) a^x$ | $\int a^xdx = \ln \|x\| + C$ |
| $\dfrac{d}{dx} \sin x = \cos x$ | $\int |
| $\dfrac{d}{dx} \cos x = -\sin x$ | |
| $\dfrac{d}{dx} \tan{x} = \sec^2 x$ | |
| $\dfrac{d}{dx} \sec x = \sec x \tan x$ | |
| $\dfrac{d}{dx} \sin^{-1} x = \dfrac{1}{\sqrt{1-x^2}}$ | |
| $\dfrac{d}{dx} \sin x = \cos x$ | $\int \cos(x) dx = \sin (x) + C$ |
| $\dfrac{d}{dx} \cos x = -\sin x$ | $\int \sin(x)dx = \sin x + C$ |
| $\dfrac{d}{dx} \tan{x} = \sec^2 x$ | $\int \sec^2(x)dx = \tan(x) + C$ |
| $\dfrac{d}{dx} \sec x = \sec x \tan x$ | $\int sec^2(x) dx = \sec(x) + C$ |
| $\dfrac{d}{dx} \sin^{-1} x = \dfrac{1}{\sqrt{1-x^2}}$ | $\int \sec(x) \tan(x) = $ |
| $\dfrac{d}{dx} \tan^{-1} x = \dfrac{1}{1+x^2}$ | |
| $\dfrac{d}{dx} k f(x) = k f'(x)$ | |
| $\dfrac{d}{dx} f(x) \pm g(x) = f'(x) \pm g'(x)$ | |