To integrate $\displaystyle \int\sqrt{a^2-x^2}$ you will let x = ...

To integrate $\displaystyle \int\sqrt{x^2-a^2}$ you will let x = ...

To integrate $\displaystyle \int\sqrt{x^2+a^2}$ you will let x = ...

I'm not sure if I'm meant to derive these or just know them. Either way, I'm screwed.