Optimal. Leaf size=13 \[ \log \left (4 e^{-1+\log ^2(x)}+x\right ) \]
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Rubi [A] time = 0.30, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.094, Rules used = {6741, 12, 6684} \begin {gather*} \log \left (e x+4 e^{\log ^2(x)}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6684
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e \left (x+8 e^{-1+\log ^2(x)} \log (x)\right )}{x \left (4 e^{\log ^2(x)}+e x\right )} \, dx\\ &=e \int \frac {x+8 e^{-1+\log ^2(x)} \log (x)}{x \left (4 e^{\log ^2(x)}+e x\right )} \, dx\\ &=\log \left (4 e^{\log ^2(x)}+e x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 13, normalized size = 1.00 \begin {gather*} \log \left (4 e^{\log ^2(x)}+e x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 12, normalized size = 0.92 \begin {gather*} \log \left (x + 4 \, e^{\left (\log \relax (x)^{2} - 1\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 13, normalized size = 1.00 \begin {gather*} \log \left (x e + 4 \, e^{\left (\log \relax (x)^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 1.00
method | result | size |
norman | \(\ln \left (x +4 \,{\mathrm e}^{\ln \relax (x )^{2}-1}\right )\) | \(13\) |
risch | \(1+\ln \left (\frac {x}{4}+{\mathrm e}^{\left (\ln \relax (x )-1\right ) \left (\ln \relax (x )+1\right )}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 12, normalized size = 0.92 \begin {gather*} \log \left (\frac {1}{4} \, x e + e^{\left (\log \relax (x)^{2}\right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.45, size = 12, normalized size = 0.92 \begin {gather*} \ln \left (x+4\,{\mathrm {e}}^{{\ln \relax (x)}^2-1}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 12, normalized size = 0.92 \begin {gather*} \log {\left (\frac {x}{4} + e^{\log {\relax (x )}^{2} - 1} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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