∫ 0 a x ∗ x 2 + a 2 d x {\displaystyle \int _{0}^{a}x*{\sqrt {x^{2}+a^{2}}}dx}
u = x 2 + a 2 d u = 2 x d x 1 2 d u = x d x {\displaystyle {\begin{aligned}u&=x^{2}+a^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=xdx\\[2ex]\end{aligned}}}
1 2 ∫ a 2 2 a 2 u ⋅ d u = 1 2 ⋅ a 1 2 + 1 1 2 + 1 | 2 a 2 a 2 {\displaystyle {\begin{aligned}{\frac {1}{2}}\int _{a^{2}}^{2a^{2}}{\sqrt {u}}\,\cdot du={\frac {1}{2}}\,\cdot {\frac {a^{{\frac {1}{2}}+1}}{{\frac {1}{2}}+1}}{\bigg |}_{2a^{2}}^{a^{2}}\end{aligned}}}
![{\displaystyle {\begin{aligned}u&=x^{2}+a^{2}\\[2ex]du&=2xdx\\[2ex]{\frac {1}{2}}du&=xdx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/b30e1c4f437286276a954ed47d027e3241e5b97c)
