Hi folks,

Could someone please tell me if $\dfrac{-1}{\sqrt{a^2 - x^2}} = \dfrac{1}{\sqrt{x^2 - a^2}}$

I think the above is true. The reason I ask is that

$\int \dfrac {- dx}{\sqrt{a^2 - x^2}} = \cos^{-1}\dfrac{x}{a}$

But

$\int \dfrac {dx}{\sqrt{x^2 - a^2}} = \cosh^{-1}\dfrac{x}{a}$

these results are clearly different. This suggests the initial statement is wrong, but I can't see why.