Solution
We solve the inequality
[tex]\begin{gathered} Let\text{ }I=\int\frac{x}{\sqrt{x^2+5}}dx \\ \\ Let\text{ }u=x^2+5 \\ \\ du=2xdx \\ \\ I=\int\frac{x}{\sqrt{x^2+5}}dx=\int\frac{1}{\sqrt{u}}\times\frac{1}{2}du \\ \\ I=\frac{1}{2}\int u^{-\frac{1}{2}}du \\ \\ I=\frac{1}{2}\times\frac{u^{\frac{1}{2}}}{\frac{1}{2}} \\ \\ I=u^{\frac{1}{2}} \\ \\ I=\sqrt{x^2+5}+C \end{gathered}[/tex]
