Optimal. Leaf size=15 \[ 3 \left (e^{\frac {3}{x^2}}-3 x\right )^2 \]
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Rubi [A]
time = 0.05, antiderivative size = 25, normalized size of antiderivative = 1.67, number of steps
used = 4, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {14, 2240, 2326}
\begin {gather*} 27 x^2-18 e^{\frac {3}{x^2}} x+3 e^{\frac {6}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2240
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {36 e^{\frac {6}{x^2}}}{x^3}+54 x-\frac {18 e^{\frac {3}{x^2}} \left (-6+x^2\right )}{x^2}\right ) \, dx\\ &=27 x^2-18 \int \frac {e^{\frac {3}{x^2}} \left (-6+x^2\right )}{x^2} \, dx-36 \int \frac {e^{\frac {6}{x^2}}}{x^3} \, dx\\ &=3 e^{\frac {6}{x^2}}-18 e^{\frac {3}{x^2}} x+27 x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 15, normalized size = 1.00 \begin {gather*} 3 \left (e^{\frac {3}{x^2}}-3 x\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 7.02, size = 24, normalized size = 1.60
method | result | size |
derivativedivides | \(27 x^{2}-18 \,{\mathrm e}^{\frac {3}{x^{2}}} x +3 \,{\mathrm e}^{\frac {6}{x^{2}}}\) | \(24\) |
default | \(27 x^{2}-18 \,{\mathrm e}^{\frac {3}{x^{2}}} x +3 \,{\mathrm e}^{\frac {6}{x^{2}}}\) | \(24\) |
risch | \(27 x^{2}-18 \,{\mathrm e}^{\frac {3}{x^{2}}} x +3 \,{\mathrm e}^{\frac {6}{x^{2}}}\) | \(24\) |
norman | \(\frac {27 x^{4}+3 x^{2} {\mathrm e}^{\frac {6}{x^{2}}}-18 \,{\mathrm e}^{\frac {3}{x^{2}}} x^{3}}{x^{2}}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.39, size = 66, normalized size = 4.40 \begin {gather*} -9 \, \sqrt {3} x \sqrt {-\frac {1}{x^{2}}} \Gamma \left (-\frac {1}{2}, -\frac {3}{x^{2}}\right ) + 27 \, x^{2} - \frac {18 \, \sqrt {3} \sqrt {\pi } {\left (\operatorname {erf}\left (\sqrt {3} \sqrt {-\frac {1}{x^{2}}}\right ) - 1\right )}}{x \sqrt {-\frac {1}{x^{2}}}} + 3 \, e^{\left (\frac {6}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 23, normalized size = 1.53 \begin {gather*} 27 \, x^{2} - 18 \, x e^{\left (\frac {3}{x^{2}}\right )} + 3 \, e^{\left (\frac {6}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 22, normalized size = 1.47 \begin {gather*} 27 x^{2} - 18 x e^{\frac {3}{x^{2}}} + 3 e^{\frac {6}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 23, normalized size = 1.53 \begin {gather*} 27 \, x^{2} - 18 \, x e^{\left (\frac {3}{x^{2}}\right )} + 3 \, e^{\left (\frac {6}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.62, size = 16, normalized size = 1.07 \begin {gather*} 3\,{\left (3\,x-{\mathrm {e}}^{\frac {3}{x^2}}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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