∫ 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 x d u = 1 1 − x 2 d x {\displaystyle {\begin{aligned}u&=4+r^{2}{x}\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\;dx\\[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}{x}\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\;dx\\[2ex]\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/8d5f8cffb422ccc58acca37f3c6c4b477d5461f2)
