Integral calculus

The fundamental theorem of calculus:

$\int \frac{df}{dx}=f$

Linearity of the integral:

$\begin{align*} \int cf(x)dx&=c\int f(x)dx \\\int [f(x)+g(x)]&=c\int f(x)dx+\int g(x)dx \end{align*}$

Integration by parts:

$\int fdg=fg-\int gdf$

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