Arctan

The $\mathrm{arctan}$ function is the inverse function of the tangent function.

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Properties

Proposition: $$\dfrac{d}{dz} \mathrm{arctan}(z) = \dfrac{1}{z^2+1}$$

Proof: █

Proposition: $$\int \mathrm{arctan}(z) = z\mathrm{arctan}(z) - \dfrac{1}{2}\log(1+z^2)+C$$

Proof: █

Proposition: $$\mathrm{arctan}(z) = \mathrm{arccot}\left( \dfrac{1}{z} \right)$$

Proof: █