∫[0,1]dx∫[0,1]dy∫[0,1]xyze^(x+y)dz
=∫[0→1]xe^xdx∫[0→1]ye^ydy∫[0→1]zdz
然后三个一个一个地做就行了
∫[0→1]zdz
=(1/2)z² |[0→1]
=1/2
∫[0→1]xe^xdx=∫[0→1]ye^ydy
=∫[0→1]xd(e^x)
=xe^x-∫[0→1] e^x dx
=xe^x-e^x |[0→1]
=e-e+1
=1
因此原式=1*1*(1/2)=1/2