Optimal. Leaf size=28 \[ \log \left (2-x+\left (x+\frac {5-x}{1-\log \left (\frac {5}{x}\right )}\right )^2\right ) \]
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Rubi [F]
time = 123.39, 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 {50-9 x+\left (-3 x+2 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-7 x-2 x^2\right ) \log ^2\left (\frac {5}{x}\right )+\left (-x+2 x^2\right ) \log ^3\left (\frac {5}{x}\right )}{-27 x+x^2+\left (31 x+7 x^2\right ) \log \left (\frac {5}{x}\right )+\left (-6 x-7 x^2-x^3\right ) \log ^2\left (\frac {5}{x}\right )+\left (2 x-x^2+x^3\right ) \log ^3\left (\frac {5}{x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
Aborted
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(70\) vs. \(2(28)=56\).
time = 0.05, size = 70, normalized size = 2.50 \begin {gather*} -2 \log \left (1-\log \left (\frac {5}{x}\right )\right )+\log \left (27-x-4 \log \left (\frac {5}{x}\right )-8 x \log \left (\frac {5}{x}\right )+2 \log ^2\left (\frac {5}{x}\right )-x \log ^2\left (\frac {5}{x}\right )+x^2 \log ^2\left (\frac {5}{x}\right )\right ) \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. \(90\) vs.
\(2(28)=56\).
time = 2.25, size = 91, normalized size = 3.25
method | result | size |
norman | \(-2 \ln \left (\ln \left (\frac {5}{x}\right )-1\right )+\ln \left (x^{2} \ln \left (\frac {5}{x}\right )^{2}-x \ln \left (\frac {5}{x}\right )^{2}-8 x \ln \left (\frac {5}{x}\right )+2 \ln \left (\frac {5}{x}\right )^{2}-x -4 \ln \left (\frac {5}{x}\right )+27\right )\) | \(69\) |
risch | \(\ln \left (x^{2}-x +2\right )-2 \ln \left (\ln \left (\frac {5}{x}\right )-1\right )+\ln \left (\ln \left (\frac {5}{x}\right )^{2}-\frac {4 \left (2 x +1\right ) \ln \left (\frac {5}{x}\right )}{x^{2}-x +2}-\frac {x -27}{x^{2}-x +2}\right )\) | \(70\) |
derivativedivides | \(-2 \ln \left (\frac {5}{x}\right )-2 \ln \left (\ln \left (\frac {5}{x}\right )-1\right )+\ln \left (\frac {50 \ln \left (\frac {5}{x}\right )^{2}}{x^{2}}-\frac {25 \ln \left (\frac {5}{x}\right )^{2}}{x}-\frac {100 \ln \left (\frac {5}{x}\right )}{x^{2}}+25 \ln \left (\frac {5}{x}\right )^{2}-\frac {200 \ln \left (\frac {5}{x}\right )}{x}+\frac {675}{x^{2}}-\frac {25}{x}\right )\) | \(91\) |
default | \(-2 \ln \left (\frac {5}{x}\right )-2 \ln \left (\ln \left (\frac {5}{x}\right )-1\right )+\ln \left (\frac {50 \ln \left (\frac {5}{x}\right )^{2}}{x^{2}}-\frac {25 \ln \left (\frac {5}{x}\right )^{2}}{x}-\frac {100 \ln \left (\frac {5}{x}\right )}{x^{2}}+25 \ln \left (\frac {5}{x}\right )^{2}-\frac {200 \ln \left (\frac {5}{x}\right )}{x}+\frac {675}{x^{2}}-\frac {25}{x}\right )\) | \(91\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 102 vs.
\(2 (24) = 48\).
time = 0.56, size = 102, normalized size = 3.64 \begin {gather*} \log \left (x^{2} - x + 2\right ) + \log \left (\frac {x^{2} \log \left (5\right )^{2} + {\left (x^{2} - x + 2\right )} \log \left (x\right )^{2} - {\left (\log \left (5\right )^{2} + 8 \, \log \left (5\right ) + 1\right )} x + 2 \, \log \left (5\right )^{2} - 2 \, {\left (x^{2} \log \left (5\right ) - x {\left (\log \left (5\right ) + 4\right )} + 2 \, \log \left (5\right ) - 2\right )} \log \left (x\right ) - 4 \, \log \left (5\right ) + 27}{x^{2} - x + 2}\right ) - 2 \, \log \left (-\log \left (5\right ) + \log \left (x\right ) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 68 vs.
\(2 (24) = 48\).
time = 0.36, size = 68, normalized size = 2.43 \begin {gather*} \log \left (x^{2} - x + 2\right ) + \log \left (\frac {{\left (x^{2} - x + 2\right )} \log \left (\frac {5}{x}\right )^{2} - 4 \, {\left (2 \, x + 1\right )} \log \left (\frac {5}{x}\right ) - x + 27}{x^{2} - x + 2}\right ) - 2 \, \log \left (\log \left (\frac {5}{x}\right ) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 90 vs.
\(2 (24) = 48\).
time = 0.52, size = 90, normalized size = 3.21 \begin {gather*} \log \left (25 \, \log \left (\frac {5}{x}\right )^{2} - \frac {25 \, \log \left (\frac {5}{x}\right )^{2}}{x} - \frac {200 \, \log \left (\frac {5}{x}\right )}{x} + \frac {50 \, \log \left (\frac {5}{x}\right )^{2}}{x^{2}} - \frac {25}{x} - \frac {100 \, \log \left (\frac {5}{x}\right )}{x^{2}} + \frac {675}{x^{2}}\right ) - 2 \, \log \left (\frac {5}{x}\right ) - 2 \, \log \left (\log \left (\frac {5}{x}\right ) - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.27, size = 173, normalized size = 6.18 \begin {gather*} 4\,\ln \left (x-5\right )-2\,\ln \left (\frac {\left (\ln \left (\frac {5}{x}\right )-1\right )\,{\left (x-5\right )}^2\,\left (-4\,x^5+49\,x^4-166\,x^3+113\,x^2+112\,x+32\right )}{x^2\,{\left (x^2-x+2\right )}^4}\right )-7\,\ln \left (x^2-x+2\right )+2\,\ln \left (4\,x^5-49\,x^4+166\,x^3-113\,x^2-112\,x-32\right )+\ln \left (\frac {-x^2\,{\ln \left (\frac {5}{x}\right )}^2+x\,{\ln \left (\frac {5}{x}\right )}^2+8\,x\,\ln \left (\frac {5}{x}\right )+x-2\,{\ln \left (\frac {5}{x}\right )}^2+4\,\ln \left (\frac {5}{x}\right )-27}{x\,\left (x^2-x+2\right )}\right )-3\,\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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