Optimal. Leaf size=23 \[ -\frac {1}{2} \log \left (2 \log \left (\frac {1}{4} x \left (e^2 x^2+\log (5)\right )\right )\right ) \]
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Rubi [A] time = 0.19, antiderivative size = 22, normalized size of antiderivative = 0.96, number of steps used = 2, number of rules used = 2, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {1593, 6684} \begin {gather*} -\frac {1}{2} \log \left (\log \left (\frac {1}{4} \left (e^2 x^3+x \log (5)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-3 e^2 x^2-\log (5)}{x \left (2 e^2 x^2+2 \log (5)\right ) \log \left (\frac {1}{4} \left (e^2 x^3+x \log (5)\right )\right )} \, dx\\ &=-\frac {1}{2} \log \left (\log \left (\frac {1}{4} \left (e^2 x^3+x \log (5)\right )\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.11, size = 21, normalized size = 0.91 \begin {gather*} -\frac {1}{2} \log \left (\log \left (\frac {1}{4} x \left (e^2 x^2+\log (5)\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.66, size = 17, normalized size = 0.74 \begin {gather*} -\frac {1}{2} \, \log \left (\log \left (\frac {1}{4} \, x^{3} e^{2} + \frac {1}{4} \, x \log \relax (5)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 22, normalized size = 0.96 \begin {gather*} -\frac {1}{2} \, \log \left (2 \, \log \relax (2) - \log \left (x^{3} e^{2} + x \log \relax (5)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.43, size = 18, normalized size = 0.78
method | result | size |
norman | \(-\frac {\ln \left (\ln \left (\frac {x \ln \relax (5)}{4}+\frac {x^{3} {\mathrm e}^{2}}{4}\right )\right )}{2}\) | \(18\) |
risch | \(-\frac {\ln \left (\ln \left (\frac {x \ln \relax (5)}{4}+\frac {x^{3} {\mathrm e}^{2}}{4}\right )\right )}{2}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 20, normalized size = 0.87 \begin {gather*} -\frac {1}{2} \, \log \left (-2 \, \log \relax (2) + \log \left (x^{2} e^{2} + \log \relax (5)\right ) + \log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 9.11, size = 17, normalized size = 0.74 \begin {gather*} -\frac {\ln \left (\ln \left (\frac {{\mathrm {e}}^2\,x^3}{4}+\frac {\ln \relax (5)\,x}{4}\right )\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 20, normalized size = 0.87 \begin {gather*} - \frac {\log {\left (\log {\left (\frac {x^{3} e^{2}}{4} + \frac {x \log {\relax (5 )}}{4} \right )} \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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