Primitive of Arccotangent Function
Jump to navigation
Jump to search
Theorem
- $\ds \int \arccot x \rd x = x \arccot x + \frac {\map \ln {x^2 + 1} } 2 + C$
Proof
From Primitive of $\arccot \dfrac x a$:
- $\ds \int \arctan \frac x a \rd x = x \arccot \frac x a + \frac a 2 \map \ln {x^2 + a^2} + C$
The result follows by setting $a = 1$.
$\blacksquare$
Also presented as
This result can also be presented as:
- $\ds \int \arccot x \rd x = x \arccot x + \ln \sqrt {x^2 + 1} + C$
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals