Primitive of Root of a squared minus x squared/Arcsine Form/Mistake

Source Work

 * Appendix $7$: Integrals
 * Appendix $7$: Integrals

Mistake

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

Correction
This should read:


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

This has been corrected in the $6$th edition.