Primitive of Arccotangent Function/Also presented as

Primitive of Arccotangent Function: Also presented as

This result can also be presented as:

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

Proof

From Primitive of $\arccot x$:

$\ds \int \arccot x \rd x = x \arccot x + \dfrac 1 2 \map \ln {x^2 + 1} + C$

The result follows by observing:

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

from Logarithm of Power.

$\blacksquare$

Sources

• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals