I would like to integrate
Integrate[x*E^(x^2 + y^2 + z^2) Boole[x^2 + y^2 + z^2 <= 1], {x,0,1}, {y,0,1}, {z,0,1}]
However Mathematica gives me
E*Integrate[x*DawsonF[Sqrt[1 - x^2 - y^2]], {x, 0, 1}, {y, 0, Sqrt[1 - x^2]}]
instead of a closed form. Using NIntegrate
does match numerically the actual answer, Pi/8
. How can I evaluate this integral without using spherical coordinates? I've tried with Assumptions -> x>=0 && y>=0 && z>=0
, but that does not help.