求助：求积分∫r^3.√(1- r^2) dr
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∫ r^3.√(1-r^2) dr
=-(1/3)∫ r^2 d(1-r^2)^(3/2)
=-(1/3)r^2.(1-r^2)^(3/2) +(2/3)∫ r (1-r^2)^(3/2) dr
=-(1/3)r^2.(1-r^2)^(3/2) -(1/3)∫ (1-r^2)^(3/2) d(1-r^2)
=-(1/3)r^2.(1-r^2)^(3/2) -(2/15)(1-r^2)^(5/2) +C
=-(1/3)∫ r^2 d(1-r^2)^(3/2)
=-(1/3)r^2.(1-r^2)^(3/2) +(2/3)∫ r (1-r^2)^(3/2) dr
=-(1/3)r^2.(1-r^2)^(3/2) -(1/3)∫ (1-r^2)^(3/2) d(1-r^2)
=-(1/3)r^2.(1-r^2)^(3/2) -(2/15)(1-r^2)^(5/2) +C
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