Optimal. Leaf size=24 \[ 16+\frac {5 x^2}{\left (\log \left (\frac {1}{e^4 x^2}\right )+\log \left (4 x^2\right )\right )^2} \]
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Rubi [F]
time = 0.06, 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 {10 x}{\log ^2\left (\frac {1}{e^4 x^2}\right )+2 \log \left (\frac {1}{e^4 x^2}\right ) \log \left (4 x^2\right )+\log ^2\left (4 x^2\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=10 \int \frac {x}{\log ^2\left (\frac {1}{e^4 x^2}\right )+2 \log \left (\frac {1}{e^4 x^2}\right ) \log \left (4 x^2\right )+\log ^2\left (4 x^2\right )} \, dx\\ &=10 \int \frac {x}{\left (4-\log \left (\frac {1}{x^2}\right )-\log \left (4 x^2\right )\right )^2} \, dx\\ &=5 \text {Subst}\left (\int \frac {1}{\left (4-\log \left (\frac {1}{x}\right )-\log (4 x)\right )^2} \, dx,x,x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.79 \begin {gather*} \frac {5 x^2}{\left (-4+\log \left (\frac {1}{x^2}\right )+\log \left (4 x^2\right )\right )^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(69\) vs.
\(2(25)=50\).
time = 11.06, size = 70, normalized size = 2.92
method | result | size |
risch | \(\frac {20 x^{2}}{64-64 \ln \left (2\right )+16 \ln \left (2\right )^{2}}\) | \(20\) |
gosper | \(\frac {5 x^{2}}{\ln \left (4 x^{2}\right )^{2}+2 \ln \left (\frac {{\mathrm e}^{-4}}{x^{2}}\right ) \ln \left (4 x^{2}\right )+\ln \left (\frac {{\mathrm e}^{-4}}{x^{2}}\right )^{2}}\) | \(45\) |
default | \(\frac {5 x^{2}}{4 \ln \left (2\right )^{2}+4 \ln \left (2\right ) \ln \left (x^{2}\right )+\ln \left (x^{2}\right )^{2}-16 \ln \left (2\right )-8 \ln \left (x^{2}\right )+4 \ln \left (\frac {1}{x^{2}}\right ) \ln \left (2\right )+2 \ln \left (\frac {1}{x^{2}}\right ) \ln \left (x^{2}\right )+16-8 \ln \left (\frac {1}{x^{2}}\right )+\ln \left (\frac {1}{x^{2}}\right )^{2}}\) | \(70\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.61, size = 17, normalized size = 0.71 \begin {gather*} \frac {5 \, x^{2}}{4 \, {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 17, normalized size = 0.71 \begin {gather*} \frac {5 \, x^{2}}{4 \, {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 0.71 \begin {gather*} \frac {5 x^{2}}{- 16 \log {\left (2 \right )} + 4 \log {\left (2 \right )}^{2} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 17, normalized size = 0.71 \begin {gather*} \frac {5 \, x^{2}}{4 \, {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) + 4\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.18, size = 11, normalized size = 0.46 \begin {gather*} \frac {5\,x^2}{{\left (\ln \left (4\right )-4\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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