Optimal. Leaf size=19 \[ e^{\frac {11}{3}+e^x+\frac {2}{x}+x}+2 x \]
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Rubi [F] time = 0.37, 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 {2 x^2+e^{\frac {6+11 x+3 e^x x+3 x^2}{3 x}} \left (-2+x^2+e^x x^2\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2+e^{\frac {11}{3}+e^x+\frac {2}{x}+2 x}+\frac {e^{\frac {11}{3}+e^x+\frac {2}{x}+x} \left (-2+x^2\right )}{x^2}\right ) \, dx\\ &=2 x+\int e^{\frac {11}{3}+e^x+\frac {2}{x}+2 x} \, dx+\int \frac {e^{\frac {11}{3}+e^x+\frac {2}{x}+x} \left (-2+x^2\right )}{x^2} \, dx\\ &=2 x+\int e^{\frac {11}{3}+e^x+\frac {2}{x}+2 x} \, dx+\int \left (e^{\frac {11}{3}+e^x+\frac {2}{x}+x}-\frac {2 e^{\frac {11}{3}+e^x+\frac {2}{x}+x}}{x^2}\right ) \, dx\\ &=2 x-2 \int \frac {e^{\frac {11}{3}+e^x+\frac {2}{x}+x}}{x^2} \, dx+\int e^{\frac {11}{3}+e^x+\frac {2}{x}+x} \, dx+\int e^{\frac {11}{3}+e^x+\frac {2}{x}+2 x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {11}{3}+e^x+\frac {2}{x}+x}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 25, normalized size = 1.32 \begin {gather*} 2 \, x + e^{\left (\frac {3 \, x^{2} + 3 \, x e^{x} + 11 \, x + 6}{3 \, x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x + e^{\left (x + \frac {2}{x} + e^{x} + \frac {11}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.22, size = 26, normalized size = 1.37
method | result | size |
risch | \(2 x +{\mathrm e}^{\frac {3 \,{\mathrm e}^{x} x +3 x^{2}+11 x +6}{3 x}}\) | \(26\) |
norman | \(\frac {x \,{\mathrm e}^{\frac {3 \,{\mathrm e}^{x} x +3 x^{2}+11 x +6}{3 x}}+2 x^{2}}{x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 15, normalized size = 0.79 \begin {gather*} 2 \, x + e^{\left (x + \frac {2}{x} + e^{x} + \frac {11}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.12, size = 18, normalized size = 0.95 \begin {gather*} 2\,x+{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{11/3}\,{\mathrm {e}}^{2/x}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 20, normalized size = 1.05 \begin {gather*} 2 x + e^{\frac {x^{2} + x e^{x} + \frac {11 x}{3} + 2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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