etions $5\mathrm{.}1$ thru $5\mathrm{.}5)$

Use a change of variables to evaluate the following definite integral.

${\displaystyle \underset{0}{\overset{2}{}}}\frac{2x}{(x^{2}1{)}^2}dx$

Determine a change of variables from x to u $.$ Choose the correct answer below.

A$.u=2x$

B$.u=x^2$

c$.u=x^{2}1$

D$.y=(x^{2}1{)}^2$

Write the integrel in terms of $u.$

${\displaystyle \underset{0}{\overset{2}{}}}\frac{2x}{(x^{2}1{)}^2}dx={\displaystyle \underset{1}{\overset{\phantom{}}{}}}du$

Evaluate the integral.

${\displaystyle \underset{0}{\overset{2}{}}}\frac{2x}{(x^{2}1{)}^2}dx=$

$($Type an exact arswer.$)$