Optimal. Leaf size=17 \[ -36+\frac {x^3}{5+3 x-\log (3)} \]
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Rubi [A] time = 0.09, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 5, number of rules used = 5, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.116, Rules used = {6, 1593, 1983, 27, 74} \begin {gather*} \frac {x^3}{3 x+5-\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 27
Rule 74
Rule 1593
Rule 1983
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {6 x^3+x^2 (15-3 \log (3))}{25+30 x+9 x^2+(-10-6 x) \log (3)+\log ^2(3)} \, dx\\ &=\int \frac {x^2 (15+6 x-3 \log (3))}{25+30 x+9 x^2+(-10-6 x) \log (3)+\log ^2(3)} \, dx\\ &=\int \frac {x^2 (6 x+3 (5-\log (3)))}{9 x^2+6 x (5-\log (3))+(-5+\log (3))^2} \, dx\\ &=\int \frac {x^2 (6 x+3 (5-\log (3)))}{(5+3 x-\log (3))^2} \, dx\\ &=\frac {x^3}{5+3 x-\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.02, size = 36, normalized size = 2.12 \begin {gather*} \frac {9 x^3-3 x (-5+\log (3))^2+(-5+\log (3))^3}{9 (5+3 x-\log (3))} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.69, size = 45, normalized size = 2.65 \begin {gather*} \frac {27 \, x^{3} - 3 \, {\left (x + 5\right )} \log \relax (3)^{2} + \log \relax (3)^{3} + 15 \, {\left (2 \, x + 5\right )} \log \relax (3) - 75 \, x - 125}{27 \, {\left (3 \, x - \log \relax (3) + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.31, size = 43, normalized size = 2.53 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {1}{9} \, x \log \relax (3) - \frac {5}{9} \, x + \frac {\log \relax (3)^{3} - 15 \, \log \relax (3)^{2} + 75 \, \log \relax (3) - 125}{27 \, {\left (3 \, x - \log \relax (3) + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.21, size = 15, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x^{3}}{\ln \relax (3)-3 x -5}\) | \(15\) |
norman | \(-\frac {x^{3}}{\ln \relax (3)-3 x -5}\) | \(15\) |
default | \(\frac {x^{2}}{3}+\frac {x \ln \relax (3)}{9}-\frac {5 x}{9}-\frac {3 \left (-\frac {\ln \relax (3)^{3}}{81}+\frac {5 \ln \relax (3)^{2}}{27}-\frac {25 \ln \relax (3)}{27}+\frac {125}{81}\right )}{5+3 x -\ln \relax (3)}\) | \(46\) |
risch | \(\frac {x \ln \relax (3)}{9}+\frac {x^{2}}{3}-\frac {5 x}{9}-\frac {\ln \relax (3)^{3}}{27 \left (\ln \relax (3)-3 x -5\right )}+\frac {5 \ln \relax (3)^{2}}{9 \left (\ln \relax (3)-3 x -5\right )}-\frac {25 \ln \relax (3)}{9 \left (\ln \relax (3)-3 x -5\right )}+\frac {125}{27 \left (\ln \relax (3)-3 x -5\right )}\) | \(69\) |
meijerg | \(\frac {\left (5-\ln \relax (3)\right )^{2} \left (\frac {x \left (\frac {9 x}{5-\ln \relax (3)}+6\right )}{\left (5-\ln \relax (3)\right ) \left (1+\frac {3 x}{5-\ln \relax (3)}\right )}-2 \ln \left (1+\frac {3 x}{5-\ln \relax (3)}\right )\right )}{9}+\frac {2 \left (5-\ln \relax (3)\right )^{3} \left (-\frac {3 x \left (-\frac {18 x^{2}}{\left (5-\ln \relax (3)\right )^{2}}+\frac {18 x}{5-\ln \relax (3)}+12\right )}{4 \left (5-\ln \relax (3)\right ) \left (1+\frac {3 x}{5-\ln \relax (3)}\right )}+3 \ln \left (1+\frac {3 x}{5-\ln \relax (3)}\right )\right )}{81 \left (-\frac {\ln \relax (3)}{3}+\frac {5}{3}\right )}\) | \(154\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.44, size = 42, normalized size = 2.47 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {1}{9} \, x {\left (\log \relax (3) - 5\right )} + \frac {\log \relax (3)^{3} - 15 \, \log \relax (3)^{2} + 75 \, \log \relax (3) - 125}{27 \, {\left (3 \, x - \log \relax (3) + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.79, size = 103, normalized size = 6.06 \begin {gather*} \frac {x^2}{3}-x\,\left (\frac {\ln \left (27\right )}{9}-\frac {2\,\ln \left (729\right )}{27}+\frac {5}{9}\right )+\frac {2\,\mathrm {atanh}\left (\frac {2\,{\left (\ln \relax (3)-5\right )}^3\,\left (18\,x-\ln \left (729\right )+30\right )}{9\,\sqrt {\ln \left (729\right )-6\,\ln \relax (3)}\,\sqrt {6\,\ln \relax (3)+\ln \left (729\right )-60}\,\left (\frac {50\,\ln \relax (3)}{3}-\frac {10\,{\ln \relax (3)}^2}{3}+\frac {2\,{\ln \relax (3)}^3}{9}-\frac {250}{9}\right )}\right )\,{\left (\ln \relax (3)-5\right )}^3}{9\,\sqrt {\ln \left (729\right )-6\,\ln \relax (3)}\,\sqrt {6\,\ln \relax (3)+\ln \left (729\right )-60}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.27, size = 42, normalized size = 2.47 \begin {gather*} \frac {x^{2}}{3} + x \left (- \frac {5}{9} + \frac {\log {\relax (3 )}}{9}\right ) + \frac {-125 - 15 \log {\relax (3 )}^{2} + \log {\relax (3 )}^{3} + 75 \log {\relax (3 )}}{81 x - 27 \log {\relax (3 )} + 135} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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