Question:
$\frac{2 x}{1+x^{2}}$
Solution:
Let $1+x^{2}=t$
$\therefore 2 x d x=d t$
$\Rightarrow \int \frac{2 x}{1+x^{2}} d x=\int \frac{1}{t} d t$
$=\log |t|+\mathrm{C}$
$=\log \left|1+x^{2}\right|+\mathrm{C}$
$=\log \left(1+x^{2}\right)+\mathrm{C}$
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