Optimal. Leaf size=16 \[ 6-x-\frac {x}{(1-4 \log (5))^2} \]
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Rubi [A] time = 0.01, antiderivative size = 23, normalized size of antiderivative = 1.44, number of steps used = 1, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {8} \begin {gather*} -\frac {2 x \left (1+8 \log ^2(5)-4 \log (5)\right )}{(1-\log (625))^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {2 x \left (1-4 \log (5)+8 \log ^2(5)\right )}{(1-\log (625))^2}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.00, size = 58, normalized size = 3.62 \begin {gather*} -\frac {2 x}{1-8 \log (5)+16 \log ^2(5)}+\frac {8 x \log (5)}{1-8 \log (5)+16 \log ^2(5)}-\frac {16 x \log ^2(5)}{1-8 \log (5)+16 \log ^2(5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 30, normalized size = 1.88 \begin {gather*} -\frac {2 \, {\left (8 \, x \log \relax (5)^{2} - 4 \, x \log \relax (5) + x\right )}}{16 \, \log \relax (5)^{2} - 8 \, \log \relax (5) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 29, normalized size = 1.81 \begin {gather*} -\frac {2 \, {\left (8 \, \log \relax (5)^{2} - 4 \, \log \relax (5) + 1\right )} x}{16 \, \log \relax (5)^{2} - 8 \, \log \relax (5) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 1.50
method | result | size |
norman | \(-\frac {2 \left (8 \ln \relax (5)^{2}-4 \ln \relax (5)+1\right ) x}{\left (4 \ln \relax (5)-1\right )^{2}}\) | \(24\) |
default | \(\frac {\left (-16 \ln \relax (5)^{2}+8 \ln \relax (5)-2\right ) x}{16 \ln \relax (5)^{2}-8 \ln \relax (5)+1}\) | \(29\) |
risch | \(-\frac {16 x \ln \relax (5)^{2}}{16 \ln \relax (5)^{2}-8 \ln \relax (5)+1}+\frac {8 x \ln \relax (5)}{16 \ln \relax (5)^{2}-8 \ln \relax (5)+1}-\frac {2 x}{16 \ln \relax (5)^{2}-8 \ln \relax (5)+1}\) | \(59\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 29, normalized size = 1.81 \begin {gather*} -\frac {2 \, {\left (8 \, \log \relax (5)^{2} - 4 \, \log \relax (5) + 1\right )} x}{16 \, \log \relax (5)^{2} - 8 \, \log \relax (5) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 29, normalized size = 1.81 \begin {gather*} -\frac {x\,\left (16\,{\ln \relax (5)}^2-8\,\ln \relax (5)+2\right )}{16\,{\ln \relax (5)}^2-8\,\ln \relax (5)+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.05, size = 27, normalized size = 1.69 \begin {gather*} \frac {x \left (- 16 \log {\relax (5 )}^{2} - 2 + 8 \log {\relax (5 )}\right )}{- 8 \log {\relax (5 )} + 1 + 16 \log {\relax (5 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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