Optimal. Leaf size=16 \[ e^{e^4} \left (3+x+x^2+\log (625)+\log (x)\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 25, normalized size of antiderivative = 1.56, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 14} \begin {gather*} e^{e^4} x^2+e^{e^4} x+e^{e^4} \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{e^4} \int \frac {1+x+2 x^2}{x} \, dx\\ &=e^{e^4} \int \left (1+\frac {1}{x}+2 x\right ) \, dx\\ &=e^{e^4} x+e^{e^4} x^2+e^{e^4} \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} e^{e^4} \left (x+x^2+\log (x)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 16, normalized size = 1.00 \begin {gather*} {\left (x^{2} + x\right )} e^{\left (e^{4}\right )} + e^{\left (e^{4}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 12, normalized size = 0.75 \begin {gather*} {\left (x^{2} + x + \log \left ({\left | x \right |}\right )\right )} e^{\left (e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 12, normalized size = 0.75
method | result | size |
default | \({\mathrm e}^{{\mathrm e}^{4}} \left (\ln \relax (x )+x^{2}+x \right )\) | \(12\) |
norman | \(x \,{\mathrm e}^{{\mathrm e}^{4}}+x^{2} {\mathrm e}^{{\mathrm e}^{4}}+{\mathrm e}^{{\mathrm e}^{4}} \ln \relax (x )\) | \(20\) |
risch | \(x \,{\mathrm e}^{{\mathrm e}^{4}}+x^{2} {\mathrm e}^{{\mathrm e}^{4}}+{\mathrm e}^{{\mathrm e}^{4}} \ln \relax (x )\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 11, normalized size = 0.69 \begin {gather*} {\left (x^{2} + x + \log \relax (x)\right )} e^{\left (e^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.41, size = 11, normalized size = 0.69 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^4}\,\left (x+\ln \relax (x)+x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 22, normalized size = 1.38 \begin {gather*} x^{2} e^{e^{4}} + x e^{e^{4}} + e^{e^{4}} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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