For the integral below, determine which integration technique you would start with on the integral. You do not need to evaluate the integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{8}{x^2-\mathrm{.}49}dx$

Algebraic manipulation $($rewriting using algebra$)$

Substitution, with $u=$

By$-$Parts, with $u=,dv=dx$

Partial Fractions

Long Division

Table entry from the mini$-$table below, # $$

Mini$-$table

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{a^2+u^2}=\frac{1}{a}ta{n}^{-1}(\frac{u}{a})+C$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{\sqrt[\phantom{2}]{a^2-u^2}}=si{n}^{-1}(\frac{u}{a})+C$

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

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{u^2\sqrt[\phantom{2}]{a^2-u^2}}=-\frac{1}{a^{2}u}\sqrt[\phantom{2}]{a^2-u^2}+C$