Evaluate the integral using the table of possible integral formulas. Show any u$-$substitutions correctly and indicate which formula is the correct one to use.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[\phantom{2}]{x^4-9}dx$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{u^2-a^2}du=\frac{u}{2}\sqrt[\phantom{2}]{u^2-a^2}-\frac{a^2}{2}ln|u\sqrt[\phantom{2}]{u^2-a^2}|C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{u}^2\sqrt[\phantom{2}]{u^2-a^2}du=\frac{u}{8}(2u^2-a^2)\sqrt[\phantom{2}]{u^2-a^2}-\frac{a^4}{8}ln|u\sqrt[\phantom{2}]{u^2-a^2}|C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{u^2-a^2}}{u}du=\sqrt[\phantom{2}]{u^2-a^2}-aco{s}^{-1}(\frac{a}{|u|})C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{u^2-a^2}}{u^2}du=-\frac{\sqrt[\phantom{2}]{u^2-a^2}}{u}ln|u\sqrt[\phantom{2}]{u^2-a^2}|C$