Optimal. Leaf size=25 \[ 3 \left (4+x^2-\frac {x^2}{\left (e^{e^{4/x}}+x\right )^2}\right ) \]
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Rubi [F] time = 1.44, 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 {6 e^{3 e^{4/x}} x+18 e^{2 e^{4/x}} x^2+6 x^4+e^{e^{4/x}} \left (-24 e^{4/x}-6 x+18 x^3\right )}{e^{3 e^{4/x}}+3 e^{2 e^{4/x}} x+3 e^{e^{4/x}} 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 {6 e^{3 e^{4/x}} x+18 e^{2 e^{4/x}} x^2+6 x^4+e^{e^{4/x}} \left (-24 e^{4/x}-6 x+18 x^3\right )}{\left (e^{e^{4/x}}+x\right )^3} \, dx\\ &=\int \left (-\frac {24 e^{e^{4/x}+\frac {4}{x}}}{\left (e^{e^{4/x}}+x\right )^3}-\frac {6 e^{e^{4/x}} x}{\left (e^{e^{4/x}}+x\right )^3}+\frac {6 e^{3 e^{4/x}} x}{\left (e^{e^{4/x}}+x\right )^3}+\frac {18 e^{2 e^{4/x}} x^2}{\left (e^{e^{4/x}}+x\right )^3}+\frac {18 e^{e^{4/x}} x^3}{\left (e^{e^{4/x}}+x\right )^3}+\frac {6 x^4}{\left (e^{e^{4/x}}+x\right )^3}\right ) \, dx\\ &=-\left (6 \int \frac {e^{e^{4/x}} x}{\left (e^{e^{4/x}}+x\right )^3} \, dx\right )+6 \int \frac {e^{3 e^{4/x}} x}{\left (e^{e^{4/x}}+x\right )^3} \, dx+6 \int \frac {x^4}{\left (e^{e^{4/x}}+x\right )^3} \, dx+18 \int \frac {e^{2 e^{4/x}} x^2}{\left (e^{e^{4/x}}+x\right )^3} \, dx+18 \int \frac {e^{e^{4/x}} x^3}{\left (e^{e^{4/x}}+x\right )^3} \, dx-24 \int \frac {e^{e^{4/x}+\frac {4}{x}}}{\left (e^{e^{4/x}}+x\right )^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 22, normalized size = 0.88 \begin {gather*} 3 x^2 \left (1-\frac {1}{\left (e^{e^{4/x}}+x\right )^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 61, normalized size = 2.44 \begin {gather*} \frac {3 \, {\left (x^{4} + 2 \, x^{3} e^{\left (e^{\frac {4}{x}}\right )} + x^{2} e^{\left (2 \, e^{\frac {4}{x}}\right )} - x^{2}\right )}}{x^{2} + 2 \, x e^{\left (e^{\frac {4}{x}}\right )} + e^{\left (2 \, e^{\frac {4}{x}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.18, size = 61, normalized size = 2.44 \begin {gather*} \frac {3 \, {\left (x^{4} + 2 \, x^{3} e^{\left (e^{\frac {4}{x}}\right )} + x^{2} e^{\left (2 \, e^{\frac {4}{x}}\right )} - x^{2}\right )}}{x^{2} + 2 \, x e^{\left (e^{\frac {4}{x}}\right )} + e^{\left (2 \, e^{\frac {4}{x}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 23, normalized size = 0.92
method | result | size |
risch | \(3 x^{2}-\frac {3 x^{2}}{\left ({\mathrm e}^{{\mathrm e}^{\frac {4}{x}}}+x \right )^{2}}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.41, size = 61, normalized size = 2.44 \begin {gather*} \frac {3 \, {\left (x^{4} + 2 \, x^{3} e^{\left (e^{\frac {4}{x}}\right )} + x^{2} e^{\left (2 \, e^{\frac {4}{x}}\right )} - x^{2}\right )}}{x^{2} + 2 \, x e^{\left (e^{\frac {4}{x}}\right )} + e^{\left (2 \, e^{\frac {4}{x}}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.92, size = 44, normalized size = 1.76 \begin {gather*} \frac {6\,x^3\,{\mathrm {e}}^{{\mathrm {e}}^{4/x}}+3\,x^2\,\left ({\mathrm {e}}^{2\,{\mathrm {e}}^{4/x}}+x^2-1\right )}{{\left (x+{\mathrm {e}}^{{\mathrm {e}}^{4/x}}\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.39, size = 31, normalized size = 1.24 \begin {gather*} 3 x^{2} - \frac {3 x^{2}}{x^{2} + 2 x e^{e^{\frac {4}{x}}} + e^{2 e^{\frac {4}{x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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