Optimal. Leaf size=26 \[ \frac {5}{-4+x-\log (3)-\log \left (-3+x-x^2-\log (4)\right )} \]
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Rubi [A]
time = 0.22, antiderivative size = 22, normalized size of antiderivative = 0.85, number of steps
used = 3, number of rules used = 3, integrand size = 169, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6820, 12,
6818} \begin {gather*} -\frac {5}{\log \left (-3 \left (x^2-x+3+\log (4)\right )\right )-x+4} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \left (-4+3 x-x^2-\log (4)\right )}{\left (3-x+x^2+\log (4)\right ) \left (4-x+\log \left (-3 \left (3-x+x^2+\log (4)\right )\right )\right )^2} \, dx\\ &=5 \int \frac {-4+3 x-x^2-\log (4)}{\left (3-x+x^2+\log (4)\right ) \left (4-x+\log \left (-3 \left (3-x+x^2+\log (4)\right )\right )\right )^2} \, dx\\ &=-\frac {5}{4-x+\log \left (-3 \left (3-x+x^2+\log (4)\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 22, normalized size = 0.85 \begin {gather*} -\frac {5}{4-x+\log \left (-3 \left (3-x+x^2+\log (4)\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 3.37, size = 25, normalized size = 0.96
method | result | size |
norman | \(-\frac {5}{\ln \left (3\right )+\ln \left (-2 \ln \left (2\right )-x^{2}+x -3\right )-x +4}\) | \(25\) |
risch | \(-\frac {5}{\ln \left (3\right )+\ln \left (-2 \ln \left (2\right )-x^{2}+x -3\right )-x +4}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.52, size = 26, normalized size = 1.00 \begin {gather*} \frac {5}{x - \log \left (3\right ) - \log \left (-x^{2} + x - 2 \, \log \left (2\right ) - 3\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 26, normalized size = 1.00 \begin {gather*} \frac {5}{x - \log \left (3\right ) - \log \left (-x^{2} + x - 2 \, \log \left (2\right ) - 3\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.33, size = 22, normalized size = 0.85 \begin {gather*} - \frac {5}{- x + \log {\left (- x^{2} + x - 3 - 2 \log {\left (2 \right )} \right )} + \log {\left (3 \right )} + 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.49, size = 26, normalized size = 1.00 \begin {gather*} \frac {5}{x - \log \left (3\right ) - \log \left (-x^{2} + x - 2 \, \log \left (2\right ) - 3\right ) - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {5\,x^2-15\,x+10\,\ln \left (2\right )+20}{{\ln \left (3\right )}^2\,\left (x^2-x+3\right )-40\,x+\ln \left (-x^2+x-2\,\ln \left (2\right )-3\right )\,\left (\ln \left (3\right )\,\left (2\,x^2-2\,x+6\right )-14\,x+2\,\ln \left (2\right )\,\left (2\,\ln \left (3\right )-2\,x+8\right )+10\,x^2-2\,x^3+24\right )-\ln \left (3\right )\,\left (2\,x^3-10\,x^2+14\,x-24\right )+2\,\ln \left (2\right )\,\left ({\ln \left (3\right )}^2-\ln \left (3\right )\,\left (2\,x-8\right )-8\,x+x^2+16\right )+27\,x^2-9\,x^3+x^4+{\ln \left (-x^2+x-2\,\ln \left (2\right )-3\right )}^2\,\left (x^2-x+2\,\ln \left (2\right )+3\right )+48} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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