Question number $17.$

Calculate the integral: ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x^2}{\sqrt[\phantom{2}]{2+x^2}}dx$

A $\frac{x}{(2+x^2{)}^{\frac{3}{2}}}-8ln|\frac{\sqrt[\phantom{2}]{2+x^2}}{\sqrt[\phantom{2}]{2}}|+C$

B $\frac{x}{(2+x^2{)}^{\frac{3}{2}}}-2ln|\frac{\sqrt[\phantom{2}]{2+x^2}}{\sqrt[\phantom{2}]{2}}|+C$

$x\sqrt[\phantom{2}]{2+x^2}-2ln|\frac{x+\sqrt[\phantom{2}]{2+x^2}}{\sqrt[\phantom{2}]{2}}|+C$

$\frac{x}{(2+x^2{)}^{\frac{3}{2}}}+2ln|\frac{\sqrt[\phantom{2}]{2+x^2}}{\sqrt[\phantom{2}]{2}}|+C$

$x\sqrt[\phantom{2}]{2+x^2}+2ln|\frac{x+\sqrt[\phantom{2}]{2+x^2}}{\sqrt[\phantom{2}]{2}}|+C$