Answer
$ \dfrac {1}{\ln 2}\ln \left( 2^{x}+2\right) +c$
Work Step by Step
$v=2^{x}+2\Rightarrow dv=2^{x}\ln 2$
$$\Rightarrow \int \dfrac {2x}{2^{x}+2}dx=\int \dfrac {1}{\ln 2}\times \dfrac {2^{x}\ln 2dx}{2^{x}+2}=\dfrac {1}{\ln 2}\int \dfrac {dv}{v}=\dfrac {1}{\ln 2}\ln v+c=\dfrac {1}{\ln 2}\ln \left( 2^{x}+2\right) +c$$
