Primitive of Arctangent Function/Also presented as

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Primitive of Arctangent Function: Also presented as

This result can also be presented as:

$\ds \int \arctan x \rd x = x \arctan x - \ln \sqrt {x^2 + 1} + C$


Proof

From Primitive of $\arccot x$:

$\ds \int \arctan x \rd x = x \arctan x - \frac {\map \ln {x^2 + 1} } 2 + C$

The result follows by observing:

$\dfrac 1 2 \log x = \log \sqrt x$

from Logarithm of Power.

$\blacksquare$


Sources