Answer
$x-2 \tan^{-1}(x/2)+C$
Work Step by Step
Let us consider $x = 2 \tan \theta $
and $dx=2 \sec^2 \theta d\theta $
Now, the given integral becomes:
$\int \dfrac{4 \tan^2 \theta }{4+4 \tan^2 \theta} d \theta = 2 \int (\sec^2 d \theta -1) d \theta$
Now, integrate and plug in $x = 2 \tan \theta $:
$2 \tan \theta -2 \theta+C=x-2 \tan^{-1}(x/2)+C$
