Optimal. Leaf size=18 \[ 1+e^{\frac {x^2}{\log (2)}}-\log \left (x^4\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 15, normalized size of antiderivative = 0.83, number of steps used = 4, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {12, 14, 2209} \begin {gather*} e^{\frac {x^2}{\log (2)}}-4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {2 e^{\frac {x^2}{\log (2)}} x^2-4 \log (2)}{x} \, dx}{\log (2)}\\ &=\frac {\int \left (2 e^{\frac {x^2}{\log (2)}} x-\frac {4 \log (2)}{x}\right ) \, dx}{\log (2)}\\ &=-4 \log (x)+\frac {2 \int e^{\frac {x^2}{\log (2)}} x \, dx}{\log (2)}\\ &=e^{\frac {x^2}{\log (2)}}-4 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.83 \begin {gather*} e^{\frac {x^2}{\log (2)}}-4 \log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.24, size = 14, normalized size = 0.78 \begin {gather*} e^{\left (\frac {x^{2}}{\log \relax (2)}\right )} - 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.30, size = 35, normalized size = 1.94 \begin {gather*} \frac {e^{\left (\frac {x^{2}}{\log \relax (2)}\right )} \log \relax (2)^{2} - 2 \, \log \relax (2)^{2} \log \left (\frac {x^{2}}{\log \relax (2)}\right )}{\log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 15, normalized size = 0.83
method | result | size |
norman | \({\mathrm e}^{\frac {x^{2}}{\ln \relax (2)}}-4 \ln \relax (x )\) | \(15\) |
risch | \({\mathrm e}^{\frac {x^{2}}{\ln \relax (2)}}-4 \ln \relax (x )\) | \(15\) |
default | \(\frac {-4 \ln \relax (2) \ln \relax (x )+{\mathrm e}^{\frac {x^{2}}{\ln \relax (2)}} \ln \relax (2)}{\ln \relax (2)}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 24, normalized size = 1.33 \begin {gather*} \frac {e^{\left (\frac {x^{2}}{\log \relax (2)}\right )} \log \relax (2) - 4 \, \log \relax (2) \log \relax (x)}{\log \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 14, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{\frac {x^2}{\ln \relax (2)}}-4\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.67 \begin {gather*} e^{\frac {x^{2}}{\log {\relax (2 )}}} - 4 \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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