Optimal. Leaf size=29 \[ e^{3+\frac {4-e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x}+x \]
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Rubi [F] time = 16.42, 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 {x^3+\exp \left (\frac {4-e^{1+e^{2 e^5}+4 x+4 x^2+e^{e^5} (2+4 x)}+3 x^2+x^3}{x^2}\right ) \left (-8+x^3+e^{1+e^{2 e^5}+4 x+4 x^2+e^{e^5} (2+4 x)} \left (2-4 x-4 e^{e^5} x-8 x^2\right )\right )}{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 \left (\frac {2 \exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right ) \left (1-2 \left (1+e^{e^5}\right ) x-4 x^2\right )}{x^3}+\frac {\exp \left (-\frac {e^{\left (1+e^{e^5}\right )^2+4 \left (1+e^{e^5}\right ) x+4 x^2}}{x^2}\right ) \left (-8 e^{3+\frac {4}{x^2}+x}+e^{\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}} x^3+e^{3+\frac {4}{x^2}+x} x^3\right )}{x^3}\right ) \, dx\\ &=2 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right ) \left (1-2 \left (1+e^{e^5}\right ) x-4 x^2\right )}{x^3} \, dx+\int \frac {\exp \left (-\frac {e^{\left (1+e^{e^5}\right )^2+4 \left (1+e^{e^5}\right ) x+4 x^2}}{x^2}\right ) \left (-8 e^{3+\frac {4}{x^2}+x}+e^{\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}} x^3+e^{3+\frac {4}{x^2}+x} x^3\right )}{x^3} \, dx\\ &=2 \int \left (\frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^3}-\frac {2 \exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right ) \left (1+e^{e^5}\right )}{x^2}-\frac {4 \exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x}\right ) \, dx+\int \left (1+\frac {e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x} \left (-8+x^3\right )}{x^3}\right ) \, dx\\ &=x+2 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^3} \, dx-8 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x} \, dx-\left (4 \left (1+e^{e^5}\right )\right ) \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^2} \, dx+\int \frac {e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x} \left (-8+x^3\right )}{x^3} \, dx\\ &=x+2 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^3} \, dx-8 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x} \, dx-\left (4 \left (1+e^{e^5}\right )\right ) \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^2} \, dx+\int \left (e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x}-\frac {8 e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x}}{x^3}\right ) \, dx\\ &=x+2 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^3} \, dx-8 \int \frac {e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x}}{x^3} \, dx-8 \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x} \, dx-\left (4 \left (1+e^{e^5}\right )\right ) \int \frac {\exp \left (4 \left (1+\frac {e^{2 e^5}}{4}\right )+\frac {4}{x^2}-\frac {e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+5 x+4 x^2+e^{e^5} (2+4 x)\right )}{x^2} \, dx+\int e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.58, size = 28, normalized size = 0.97 \begin {gather*} e^{3-\frac {-4+e^{\left (1+e^{e^5}+2 x\right )^2}}{x^2}+x}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 45, normalized size = 1.55 \begin {gather*} x + e^{\left (\frac {x^{3} + 3 \, x^{2} - e^{\left (4 \, x^{2} + 2 \, {\left (2 \, x + 1\right )} e^{\left (e^{5}\right )} + 4 \, x + e^{\left (2 \, e^{5}\right )} + 1\right )} + 4}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^{3} + {\left (x^{3} - 2 \, {\left (4 \, x^{2} + 2 \, x e^{\left (e^{5}\right )} + 2 \, x - 1\right )} e^{\left (4 \, x^{2} + 2 \, {\left (2 \, x + 1\right )} e^{\left (e^{5}\right )} + 4 \, x + e^{\left (2 \, e^{5}\right )} + 1\right )} - 8\right )} e^{\left (\frac {x^{3} + 3 \, x^{2} - e^{\left (4 \, x^{2} + 2 \, {\left (2 \, x + 1\right )} e^{\left (e^{5}\right )} + 4 \, x + e^{\left (2 \, e^{5}\right )} + 1\right )} + 4}{x^{2}}\right )}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 47, normalized size = 1.62
method | result | size |
risch | \(x +{\mathrm e}^{\frac {-{\mathrm e}^{4 x \,{\mathrm e}^{{\mathrm e}^{5}}+4 x^{2}+{\mathrm e}^{2 \,{\mathrm e}^{5}}+2 \,{\mathrm e}^{{\mathrm e}^{5}}+4 x +1}+x^{3}+3 x^{2}+4}{x^{2}}}\) | \(47\) |
norman | \(\frac {x^{3}+x^{2} {\mathrm e}^{\frac {-{\mathrm e}^{{\mathrm e}^{2 \,{\mathrm e}^{5}}+\left (4 x +2\right ) {\mathrm e}^{{\mathrm e}^{5}}+4 x^{2}+4 x +1}+x^{3}+3 x^{2}+4}{x^{2}}}}{x^{2}}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 43, normalized size = 1.48 \begin {gather*} x + e^{\left (x - \frac {e^{\left (4 \, x^{2} + 4 \, x e^{\left (e^{5}\right )} + 4 \, x + e^{\left (2 \, e^{5}\right )} + 2 \, e^{\left (e^{5}\right )} + 1\right )}}{x^{2}} + \frac {4}{x^{2}} + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.30, size = 50, normalized size = 1.72 \begin {gather*} x+{\mathrm {e}}^{-\frac {{\mathrm {e}}^{4\,x\,{\mathrm {e}}^{{\mathrm {e}}^5}}\,{\mathrm {e}}^{4\,x}\,\mathrm {e}\,{\mathrm {e}}^{{\mathrm {e}}^{2\,{\mathrm {e}}^5}}\,{\mathrm {e}}^{2\,{\mathrm {e}}^{{\mathrm {e}}^5}}\,{\mathrm {e}}^{4\,x^2}}{x^2}}\,{\mathrm {e}}^3\,{\mathrm {e}}^{\frac {4}{x^2}}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.57, size = 44, normalized size = 1.52 \begin {gather*} x + e^{\frac {x^{3} + 3 x^{2} - e^{4 x^{2} + 4 x + \left (4 x + 2\right ) e^{e^{5}} + 1 + e^{2 e^{5}}} + 4}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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