calculus - What are $intsqrt{a^2-x^2},textrm{d}x, intsqrt{x^2+a^2},textrm{d}x,intsqrt{x^2-a^2},textrm{d}x$?

Can someone confirm these equations below? I got it from my college textbook, unfortunately there are no proofs and more importantly I cannot seem to find any other sources that say have these equations.

$\displaystyle\int\sqrt{a^2-x^2}\,\textrm{dx}=\frac{x\sqrt{a^2-x^2}}{2}+\frac{a^2}{2}\sin^{-1}\left(\frac{x}{a}\right) + C$

$\displaystyle\int\sqrt{x^2+a^2}\,\text{dx}=\frac{x\sqrt{x^2+a^2}}{2}+\frac{a^2}{2}\ln\left(x+\sqrt{x^2+a^2}\right)+C$

$\displaystyle\int\sqrt{x^2-a^2}\,\textrm{dx}=\frac{x\sqrt{x^2-a^2}}{2}-\frac{a^2}{2}\ln\left(x+\sqrt{x^2-a^2}\right)+C$