$\int \frac{d x}{2+x^{2}}=?$

$\tan ^{-1} \frac{x}{2}+k$

$\tan ^{-1} \frac{x}{\sqrt{2}}+k$

$\sin ^{-1} \frac{x}{\sqrt{2}}+k$

$\frac{1}{\sqrt{2}} \tan ^{-1} \frac{x}{\sqrt{2}}+k$

$\frac{1}{\sqrt{2}} \sin ^{-1} \frac{x}{\sqrt{2}}+k$