Compute ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{8}{16+25x^2}dx$

Step $1$: The integral can be written in the form

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{a}{b}(\frac{1}{1+(cx{)}^2})$ where

$a=$

$b=$

$c=$

Step $2$: Use a u$-$substitution with $u=$ and $du=$

$dx$

Step $3$: Use the u$-$substitution with the form of step $1$ to write

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{8}{16+25x^2}dx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}du$

$=,+C($ use variable $u)$

$=,+C($ use variable $x)$