Optimal. Leaf size=37 \[ \frac {2}{\sqrt {3-x} \sqrt {-2+x}}-\frac {4 \sqrt {3-x}}{\sqrt {-2+x}} \]
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Rubi [A]
time = 0.00, antiderivative size = 37, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {47, 37}
\begin {gather*} \frac {2}{\sqrt {3-x} \sqrt {x-2}}-\frac {4 \sqrt {3-x}}{\sqrt {x-2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 37
Rule 47
Rubi steps
\begin {align*} \int \frac {1}{(3-x)^{3/2} (-2+x)^{3/2}} \, dx &=\frac {2}{\sqrt {3-x} \sqrt {-2+x}}+2 \int \frac {1}{\sqrt {3-x} (-2+x)^{3/2}} \, dx\\ &=\frac {2}{\sqrt {3-x} \sqrt {-2+x}}-\frac {4 \sqrt {3-x}}{\sqrt {-2+x}}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 21, normalized size = 0.57 \begin {gather*} \frac {2 (-5+2 x)}{\sqrt {-6+5 x-x^2}} \end {gather*}
Antiderivative was successfully verified.
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Mathics [C] Result contains higher order function than in optimal. Order 9 vs. order 2 in
optimal.
time = 3.25, size = 78, normalized size = 2.11 \begin {gather*} \text {Piecewise}\left [\left \{\left \{\frac {I \left (10-4 x\right )}{\sqrt {-3+x} \sqrt {-2+x}},\text {Abs}\left [-2+x\right ]>1\right \}\right \},\frac {-4 \left (-2+x\right ) \sqrt {3-x}}{\left (-2+x\right )^{\frac {3}{2}}-\sqrt {-2+x}}+\frac {2 \sqrt {3-x}}{\left (-2+x\right )^{\frac {3}{2}}-\sqrt {-2+x}}\right ] \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.16, size = 30, normalized size = 0.81
method | result | size |
gosper | \(\frac {4 x -10}{\sqrt {3-x}\, \sqrt {-2+x}}\) | \(20\) |
default | \(\frac {2}{\sqrt {3-x}\, \sqrt {-2+x}}-\frac {4 \sqrt {3-x}}{\sqrt {-2+x}}\) | \(30\) |
risch | \(\frac {2 \sqrt {\left (-2+x \right ) \left (3-x \right )}\, \left (2 x -5\right )}{\sqrt {3-x}\, \sqrt {-2+x}\, \sqrt {-\left (-3+x \right ) \left (-2+x \right )}}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 30, normalized size = 0.81 \begin {gather*} \frac {4 \, x}{\sqrt {-x^{2} + 5 \, x - 6}} - \frac {10}{\sqrt {-x^{2} + 5 \, x - 6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.30, size = 29, normalized size = 0.78 \begin {gather*} -\frac {2 \, {\left (2 \, x - 5\right )} \sqrt {x - 2} \sqrt {-x + 3}}{x^{2} - 5 \, x + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.28, size = 100, normalized size = 2.70 \begin {gather*} \begin {cases} - \frac {4 i \sqrt {x - 3} \left (x - 2\right )}{\left (x - 2\right )^{\frac {3}{2}} - \sqrt {x - 2}} + \frac {2 i \sqrt {x - 3}}{\left (x - 2\right )^{\frac {3}{2}} - \sqrt {x - 2}} & \text {for}\: \left |{x - 2}\right | > 1 \\- \frac {4 \sqrt {3 - x} \left (x - 2\right )}{\left (x - 2\right )^{\frac {3}{2}} - \sqrt {x - 2}} + \frac {2 \sqrt {3 - x}}{\left (x - 2\right )^{\frac {3}{2}} - \sqrt {x - 2}} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 71, normalized size = 1.92 \begin {gather*} 2 \left (\frac {\sqrt {-x+3}}{-2 \sqrt {x-2}+2}-\frac {-2 \sqrt {x-2}+2}{4 \sqrt {-x+3}}-\frac {\sqrt {-x+3} \sqrt {x-2}}{x-2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.25, size = 32, normalized size = 0.86 \begin {gather*} -\frac {4\,x\,\sqrt {3-x}-10\,\sqrt {3-x}}{\sqrt {x-2}\,\left (x-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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