Primitive of Root of x squared minus a squared/Inverse Hyperbolic Cosine Form/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.)

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.)

Table 2 Integrals

Mistake

$\ds \int \sqrt {x^2 - a^2} \rd x = \frac 1 2 a^2 \cosh^{-1} \frac x a + \frac 1 2 {x \sqrt {x^2 - a^2} } + C$

Correction

Should be:

$\ds \int \sqrt {x^2 - a^2} \rd x = \frac {x \sqrt {x^2 - a^2} } 2 - \frac {a^2} 2 \cosh^{-1} \frac x a + C$

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