被积区域是0
= ∫(0,1)dx∫(0,1-x)dy∫(0,1-x-y)[1/(1+x+y+z)³]dz
= ∫(0,1)dx∫(0,1-x)dy * (-1/2) * [1/(1+x+y+1-x-y)² - 1/(1+x+y)²]
= ∫(0,1)dx∫(0,1-x)dy * (1/[2(1+x+y)²] - 1/8)
= ∫(0,1)dx * (-1/[2(1+x+y)] - y/8)|(0,1-x)
= ∫(0,1)dx * [1/(2+2x) + x/8 - 3/8]
= [1/2 * ln(1+x) + x²/16 - 3x/8]|(0,1)
= (ln2)/2 - 5/16
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024