Optimal. Leaf size=23 \[ \frac {x^3}{\left (12 e^{-e^{\frac {3}{x^2}}}-x\right )^2} \]
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Rubi [F] time = 2.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^{3 e^{\frac {3}{x^2}}} x^3+e^{2 e^{\frac {3}{x^2}}} \left (144 e^{\frac {3}{x^2}}-36 x^2\right )}{-1728+432 e^{e^{\frac {3}{x^2}}} x-36 e^{2 e^{\frac {3}{x^2}}} x^2+e^{3 e^{\frac {3}{x^2}}} x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{2 e^{\frac {3}{x^2}}} \left (-144 e^{\frac {3}{x^2}}+36 x^2-e^{e^{\frac {3}{x^2}}} x^3\right )}{\left (12-e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx\\ &=\int \left (\frac {144 e^{2 e^{\frac {3}{x^2}}+\frac {3}{x^2}}}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3}+\frac {e^{2 e^{\frac {3}{x^2}}} x^2 \left (-36+e^{e^{\frac {3}{x^2}}} x\right )}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3}\right ) \, dx\\ &=144 \int \frac {e^{2 e^{\frac {3}{x^2}}+\frac {3}{x^2}}}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx+\int \frac {e^{2 e^{\frac {3}{x^2}}} x^2 \left (-36+e^{e^{\frac {3}{x^2}}} x\right )}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx\\ &=144 \int \frac {e^{2 e^{\frac {3}{x^2}}+\frac {3}{x^2}}}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx+\int \left (-\frac {24 e^{2 e^{\frac {3}{x^2}}} x^2}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3}+\frac {e^{2 e^{\frac {3}{x^2}}} x^2}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^2}\right ) \, dx\\ &=-\left (24 \int \frac {e^{2 e^{\frac {3}{x^2}}} x^2}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx\right )+144 \int \frac {e^{2 e^{\frac {3}{x^2}}+\frac {3}{x^2}}}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^3} \, dx+\int \frac {e^{2 e^{\frac {3}{x^2}}} x^2}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.38, size = 30, normalized size = 1.30 \begin {gather*} \frac {e^{2 e^{\frac {3}{x^2}}} x^3}{\left (-12+e^{e^{\frac {3}{x^2}}} x\right )^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.58, size = 40, normalized size = 1.74 \begin {gather*} \frac {x^{3} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )}}{x^{2} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )} - 24 \, x e^{\left (e^{\left (\frac {3}{x^{2}}\right )}\right )} + 144} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.56, size = 40, normalized size = 1.74 \begin {gather*} \frac {x^{3} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )}}{x^{2} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )} - 24 \, x e^{\left (e^{\left (\frac {3}{x^{2}}\right )}\right )} + 144} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 30, normalized size = 1.30
method | result | size |
risch | \(x +\frac {24 \left (x \,{\mathrm e}^{{\mathrm e}^{\frac {3}{x^{2}}}}-6\right ) x}{\left (x \,{\mathrm e}^{{\mathrm e}^{\frac {3}{x^{2}}}}-12\right )^{2}}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.42, size = 40, normalized size = 1.74 \begin {gather*} \frac {x^{3} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )}}{x^{2} e^{\left (2 \, e^{\left (\frac {3}{x^{2}}\right )}\right )} - 24 \, x e^{\left (e^{\left (\frac {3}{x^{2}}\right )}\right )} + 144} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.53, size = 26, normalized size = 1.13 \begin {gather*} \frac {x^3\,{\mathrm {e}}^{2\,{\mathrm {e}}^{\frac {3}{x^2}}}}{{\left (x\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {3}{x^2}}}-12\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.31, size = 44, normalized size = 1.91 \begin {gather*} x + \frac {24 x^{2} e^{e^{\frac {3}{x^{2}}}} - 144 x}{x^{2} e^{2 e^{\frac {3}{x^{2}}}} - 24 x e^{e^{\frac {3}{x^{2}}}} + 144} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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