∫ 0 1 r 3 4 + r 2 ⋅ d r {\displaystyle \int _{0}^{1}{\frac {r^{3}}{\sqrt {4+r^{2}}}}\cdot dr}
u = 4 + r 2 r 2 = u − 4 2 r ⋅ d r = d u ; d r d u = 1 1 − x 2 {\displaystyle {\begin{aligned}u&=4+r^{2}\\[2ex]r^{2}&=u-4\\[2ex]2r\cdot dr&=du;dr\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\ \\[2ex]\end{aligned}}}
∫ 0 1 r 3 4 + r 2 ⋅ d r = ∫ 0 1 r 3 ⋅ 1 4 + r 2 ⋅ d r {\displaystyle \int _{0}^{1}{\frac {r^{3}}{\sqrt {4+r^{2}}}}\cdot dr~~~=~~~\int _{0}^{1}r^{3}\cdot {\frac {1}{\sqrt {4+r^{2}}}}\cdot dr}
![{\displaystyle {\begin{aligned}u&=4+r^{2}\\[2ex]r^{2}&=u-4\\[2ex]2r\cdot dr&=du;dr\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\ \\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/70d1a99238a2f139b9ae186d7c1e57b592ef862a)
