Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 14

$\int \frac{du}{u\sqrt {u^2- a^2}}$ $u=x$ $a=2$

Try it: $u=x$ $du=dx$ $\int \frac{du}{u\sqrt {u^2- a^2}}=\frac 1 a arcscec \frac {|u|}{a} +C $ $\frac 1 2 arcsec \frac {|x|}2 +C$ $\int \frac{du}{u\sqrt {u^2- a^2}}$ $u=x$ $a=2$