Some integrands tested on Mathematica 7.0 and with Rubi and Maple 14
Tested by Nasser M. Abbasi, july 3, 2010
Martin posted this on sci.math.sybolic
"Here is a small gallery of fairly simple algebraic integrands on which I
have found Derive 6.10 to fail (as in an earlier example, more or less
obvious transformations on part of the operator help it succeed though):
INT(1/(SQRT(x^2+1)+2*x)^2,x)
INT(1/(SQRT(x^2-1)*(3*x^2-4)^2),x)
INT(1/(2*SQRT(x)+SQRT(x+1))^2,x)
INT(SQRT(x^2-1)/(x-#i)^2,x)
INT(1/(SQRT(x^2-1)*(x^2+1)^2),x)
INT(1/(SQRT(x-1)*(SQRT(x-1)+2*SQRT(x))^2),x)
INT(1/(SQRT(x^2-1)*(SQRT(x^2-1)+SQRT(x))^2),x)
INT(SQRT(SQRT(x^4+1)+x^2)/((x+1)^2*SQRT(x^4+1)),x)
INT(((x-1)^(3/2)+(x+1)^(3/2))/((x+1)^(3/2)*(x-1)^(3/2)),x)
Martin."
First, I downloaded Rubi from Albert web site, and loaded the Rubi package into mathematica, then run the tests below.
This notebook can be downloaded from here
Maple 14 notebook is here
Maple 14 HTML output is here
Sage 4.4 HTML worksheet is here
Result #1
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Result #2
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Result #3
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Result #5
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Result #6
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Result #7
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Result #8
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Result #9
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