Indefinite Integration

$\frac{1}{2} \sec ^{-1}\left(x^2+2\right)+C$

$-\operatorname{cosech}^{-1}\left(x^2+2\right)+C$

$\frac{1}{2} \tan ^{-1}\left(x+\frac{2}{x}\right)+C$

$-\frac{1}{2} \cot ^{-1}\left(x+\frac{2}{x}\right)+C$