$x y z$

$xyz$

$1-x-y$

$1-x-y$

$10-x^2-y^2$

$10-x^2-y^2$

$x^2$

$x^2$

$x$

$x$

$0$

$0$

$1$

$1$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{MultiInt}\right]\left(\,z\=..\,y\=..\,x\=..\,\mathrm{output}\=\mathrm{integral}\right)$

${\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}xyz\ⅆz\ⅆy\ⅆx$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{MultiInt}\right]\left(\,z\=..\,y\=..\,x\=..\right)$

$\frac{26081}{15120}$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{MultiInt}\right]\left(\,z\=..\,y\=..\,x\=..\,\mathrm{output}\=\mathrm{steps}\right)$

$\begin{array}{ccc}\multicolumn{3}{c}{{\int }_0^1{\int }_{x^2}^x{\int }_{1-x-y}^{10-x^2-y^2}xyz\ⅆz\ⅆy\ⅆx}\\ & \text{=}& {\int }_0^1{\int }_{x^2}^x\left(\genfrac{}{}{0ex}{}{\frac{xy{z}^2}{2}}{\phantom{z=1-x-y..10-x^2-y^2}}|\genfrac{}{}{0ex}{}{\phantom{\frac{xy{z}^2}{2}}}{z=1-x-y..10-x^2-y^2}\right)\ⅆy\ⅆx\hfill \\ & \text{=}& {\int }_0^1{\int }_{x^2}^x\frac{xy\left({\left(10-x^2-y^2\right)}^2-{\left(1-x-y\right)}^2\right)}{2}\ⅆy\ⅆx\hfill \\ & \text{=}& {\int }_0^1\left(\genfrac{}{}{0ex}{}{\frac{x\left(\frac{y^6}{6}+\frac{\left(-21+2x^2\right)y^4}{4}+\frac{\left(2-2x\right)y^3}{3}+\frac{\left({\left(10-x^2\right)}^2-{\left(1-x\right)}^2\right)y^2}{2}\right)}{2}}{\phantom{y=x^2..x}}|\genfrac{}{}{0ex}{}{\phantom{\frac{x\left(\frac{y^6}{6}+\frac{\left(-21+2x^2\right)y^4}{4}+\frac{\left(2-2x\right)y^3}{3}+\frac{\left({\left(10-x^2\right)}^2-{\left(1-x\right)}^2\right)y^2}{2}\right)}{2}}}{y=x^2..x}\right)\ⅆx\hfill \\ & \text{=}& {\int }_0^1\left(\frac{x\left(x^6-x^{12}\right)}{12}+\frac{x\left(-21+2x^2\right)\left(x^4-x^8\right)}{8}+\frac{x\left(2-2x\right)\left(x^3-x^6\right)}{6}+\frac{x\left({\left(10-x^2\right)}^2-{\left(1-x\right)}^2\right)\left(x^2-x^4\right)}{4}\right)\ⅆx\hfill \\ & \text{=}& \genfrac{}{}{0ex}{}{\left(-\frac{1}{168}{x}^{14}+\frac{11}{16}{x}^8-\frac{1}{48}{x}^{12}+\frac{19}{80}{x}^{10}-\frac{791}{144}{x}^6+\frac{1}{27}{x}^9+\frac{1}{6}{x}^5-\frac{1}{14}{x}^7+\frac{99}{16}{x}^4\right)}{\phantom{x=0..1}}|\genfrac{}{}{0ex}{}{\phantom{\left(-\frac{1}{168}{x}^{14}+\frac{11}{16}{x}^8-\frac{1}{48}{x}^{12}+\frac{19}{80}{x}^{10}-\frac{791}{144}{x}^6+\frac{1}{27}{x}^9+\frac{1}{6}{x}^5-\frac{1}{14}{x}^7+\frac{99}{16}{x}^4\right)}}{x=0..1}\hfill \end{array}$

$\frac{26081}{15120}$