Talk:Primitive of x squared by Root of a squared minus x squared

From ProofWiki
Jump to navigation Jump to search

I've actually taken a good look at this. Although Schaum has $\arcsin$, I still make it $\sinh^{-1}$.

The result that gives the $\sinh^{-1}$ was actually $\arctan$ in the original $14.120$, and arises from $\displaystyle \int \dfrac {\d u} {\sqrt {x^2 + c^2} }$, which in turn arises from $\displaystyle \int \dfrac {\d u} {\sqrt {x^2 - c^2} }$ for the case where $c^2 < 0$.

So Schaum appears to be wrong in $14.120$ and then wrong again here.

Another pair of eyes would be good. --prime mover (talk) 15:05, 14 August 2019 (EDT)

Wolfram seems to say $\arcsin$ (the $\arctan$ being equivalent to $\arcsin \dfrac x a$) I'll have a look at it tomorrow. Caliburn (talk) 17:16, 14 August 2019 (EDT)