Optimal. Leaf size=23 \[ \frac {2 (-2+x) x}{9 (4+4 x) (-x+\log (2))} \]
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Rubi [A] time = 0.14, antiderivative size = 34, normalized size of antiderivative = 1.48, number of steps used = 4, number of rules used = 4, integrand size = 68, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {1680, 12, 1814, 8} \begin {gather*} -\frac {\log (4)-2 x (3-\log (2))}{36 \left (x^2+x (1-\log (2))-\log (2)\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 12
Rule 1680
Rule 1814
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {-8 x^2 (3-\log (2))-2 (3-\log (2)) (1+\log (2))^2+8 x \left (3+\log ^2(2)-\log (4)\right )}{9 \left (4 x^2-(1+\log (2))^2\right )^2} \, dx,x,x+\frac {1}{72} (36-36 \log (2))\right )\\ &=\frac {1}{9} \operatorname {Subst}\left (\int \frac {-8 x^2 (3-\log (2))-2 (3-\log (2)) (1+\log (2))^2+8 x \left (3+\log ^2(2)-\log (4)\right )}{\left (4 x^2-(1+\log (2))^2\right )^2} \, dx,x,x+\frac {1}{72} (36-36 \log (2))\right )\\ &=\frac {2 x (3-\log (2))-\log (4)}{36 \left (x^2+x (1-\log (2))-\log (2)\right )}+\frac {\operatorname {Subst}\left (\int 0 \, dx,x,x+\frac {1}{72} (36-36 \log (2))\right )}{18 (1+\log (2))^2}\\ &=\frac {2 x (3-\log (2))-\log (4)}{36 \left (x^2+x (1-\log (2))-\log (2)\right )}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.09, size = 51, normalized size = 2.22 \begin {gather*} \frac {\frac {3 \log ^2(2)-\log ^3(2)+\log (4)-\log (2) \log (4)}{x-\log (2)}+\frac {3+\log (8)}{1+x}}{18 (1+\log (2))^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 26, normalized size = 1.13 \begin {gather*} -\frac {{\left (x + 1\right )} \log \relax (2) - 3 \, x}{18 \, {\left (x^{2} - {\left (x + 1\right )} \log \relax (2) + x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 28, normalized size = 1.22 \begin {gather*} -\frac {x \log \relax (2) - 3 \, x + \log \relax (2)}{18 \, {\left (x^{2} - x \log \relax (2) + x - \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 28, normalized size = 1.22
method | result | size |
norman | \(\frac {\left (\frac {\ln \relax (2)}{18}-\frac {1}{6}\right ) x +\frac {\ln \relax (2)}{18}}{\left (x +1\right ) \left (\ln \relax (2)-x \right )}\) | \(28\) |
gosper | \(\frac {x \ln \relax (2)+\ln \relax (2)-3 x}{18 x \ln \relax (2)-18 x^{2}+18 \ln \relax (2)-18 x}\) | \(30\) |
risch | \(\frac {\left (\frac {\ln \relax (2)}{18}-\frac {1}{6}\right ) x +\frac {\ln \relax (2)}{18}}{x \ln \relax (2)-x^{2}+\ln \relax (2)-x}\) | \(32\) |
default | \(-\frac {\ln \relax (2) \left (\ln \relax (2)-2\right )}{18 \left (1+\ln \relax (2)\right ) \left (x -\ln \relax (2)\right )}+\frac {1}{6 \left (1+\ln \relax (2)\right ) \left (x +1\right )}\) | \(37\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 28, normalized size = 1.22 \begin {gather*} -\frac {x {\left (\log \relax (2) - 3\right )} + \log \relax (2)}{18 \, {\left (x^{2} - x {\left (\log \relax (2) - 1\right )} - \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 30, normalized size = 1.30 \begin {gather*} \frac {\ln \relax (2)+x\,\left (\ln \relax (2)-3\right )}{-18\,x^2+\left (18\,\ln \relax (2)-18\right )\,x+18\,\ln \relax (2)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 29, normalized size = 1.26 \begin {gather*} - \frac {x \left (-3 + \log {\relax (2 )}\right ) + \log {\relax (2 )}}{18 x^{2} + x \left (18 - 18 \log {\relax (2 )}\right ) - 18 \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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