g ( r ) = ∫ 0 r x 2 + 4 d x d d r ( g ( r ) ) = d d r [ ∫ 0 r x 2 + 4 d x ] = 1 ⋅ ( r ) 2 + 4 − 0 ⋅ ( 0 ) 2 + 4 = r 2 + 4 {\displaystyle {\begin{aligned}g(r)=\int _{0}^{r}{\sqrt {x^{2}+4}}\,dx\\{\frac {d}{dr}}(g(r))={\frac {d}{dr}}\left[\int _{0}^{r}{\sqrt {x^{2}+4}}\,dx\right]=1\cdot {\sqrt {(r)^{2}+4}}-0\cdot {\sqrt {(0)^{2}+4}}={\sqrt {r^{2}+4}}\end{aligned}}}
![{\displaystyle {\begin{aligned}g(r)=\int _{0}^{r}{\sqrt {x^{2}+4}}\,dx\\{\frac {d}{dr}}(g(r))={\frac {d}{dr}}\left[\int _{0}^{r}{\sqrt {x^{2}+4}}\,dx\right]=1\cdot {\sqrt {(r)^{2}+4}}-0\cdot {\sqrt {(0)^{2}+4}}={\sqrt {r^{2}+4}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6d89de24cc5020a93ad5066dcfc5bc2325ab5a80)