Question

$$\displaystyle\int{ \frac{ \sqrt{ { x }^{ 2 } +1 } }{ { x }^{ 2 } } }d x$$

Evaluate

$-\frac{\ln(|\frac{x}{\sqrt{x^{2}+1}}-1|)}{2}+\frac{\ln(|-\frac{x}{\sqrt{x^{2}+1}}-1|)}{2}-\frac{\sqrt{x^{2}+1}}{x}+С$

Differentiate w.r.t. x

$\frac{\sqrt{x^{2}+1}}{x^{2}}$