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Question: Why can't Maple evaluate this triple integral in the rectangular coordinate system?

Question:Why can't Maple evaluate this triple integral in the rectangular coordinate system?

DJJerome1976 540 Maple 16
integral
April 03 2013
0

I'm trying to evaluate this triple integral in the rectangular coordinate system and Maple appears to be stuck after the second iterated integral. I then tried to evaluate the same integral in another computer algebra system and got the answer almost instantaneously. My guess is that system converted it to an integral in the cylindrical coordinate system. Why does Maple not do the same? Is there a way to force Maple to do so without manually doing the conversion? I hope there isn't a typo that I'm missing.

with(VectorCalculus):

int(int(int(sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(1, x^2), y^2)), z = -1 .. 2), y = VectorCalculus:-`-`(sqrt(VectorCalculus:-`+`(8, VectorCalculus:-`-`(x^2)))) .. sqrt(VectorCalculus:-`+`(8, VectorCalculus:-`-`(x^2)))), x = 0 .. VectorCalculus:-`*`(2, sqrt(2)))

int(9*(8-x^2)^(1/2)-(3/2)*ln(-(8-x^2)^(1/2)+3)-(3/2)*ln(-(8-x^2)^(1/2)+3)*x^2+(3/2)*ln((8-x^2)^(1/2)+3)+(3/2)*ln((8-x^2)^(1/2)+3)*x^2, x = 0 .. 2*2^(1/2))

 (1)

int(sqrt(VectorCalculus:-`+`(VectorCalculus:-`+`(1, x^2), y^2)), [x, y, z] = Region(0 .. VectorCalculus:-`*`(2, sqrt(2)), VectorCalculus:-`-`(sqrt(VectorCalculus:-`+`(8, VectorCalculus:-`-`(x^2)))) .. sqrt(VectorCalculus:-`+`(8, VectorCalculus:-`-`(x^2))), -1 .. 2))

int(9*(8-x^2)^(1/2)-(3/2)*ln(-(8-x^2)^(1/2)+3)-(3/2)*ln(-(8-x^2)^(1/2)+3)*x^2+(3/2)*ln((8-x^2)^(1/2)+3)+(3/2)*ln((8-x^2)^(1/2)+3)*x^2, x = 0 .. 2*2^(1/2))

 (2)

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