Optimal. Leaf size=19 \[ 5 \left (-3+(2+x) \left (x+\left (-\frac {9}{5}+x+\log (3)\right )^4\right )\right ) \]
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Rubi [B] time = 0.04, antiderivative size = 110, normalized size of antiderivative = 5.79, number of steps used = 4, number of rules used = 1, integrand size = 73, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {12} \begin {gather*} 5 x^5-26 x^4+20 x^4 \log (3)+\frac {126 x^3}{5}+30 x^3 \log ^2(3)-68 x^3 \log (3)+\frac {2069 x^2}{25}-48 x^2 \log ^2(3)-\frac {108}{5} x^2 \log (3)-\frac {1}{125} x \left (21349-625 \log ^4(3)\right )+\frac {1}{5} (10 x+1)^2 \log ^3(3)-\frac {594}{5} x \log ^2(3)+\frac {6804}{25} x \log (3) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{125} \int \left (-21349+20690 x+9450 x^2-13000 x^3+3125 x^4+\left (34020-5400 x-25500 x^2+10000 x^3\right ) \log (3)+\left (-14850-12000 x+11250 x^2\right ) \log ^2(3)+(500+5000 x) \log ^3(3)+625 \log ^4(3)\right ) \, dx\\ &=\frac {2069 x^2}{25}+\frac {126 x^3}{5}-26 x^4+5 x^5+\frac {1}{5} (1+10 x)^2 \log ^3(3)-\frac {1}{125} x \left (21349-625 \log ^4(3)\right )+\frac {1}{125} \log (3) \int \left (34020-5400 x-25500 x^2+10000 x^3\right ) \, dx+\frac {1}{125} \log ^2(3) \int \left (-14850-12000 x+11250 x^2\right ) \, dx\\ &=\frac {2069 x^2}{25}+\frac {126 x^3}{5}-26 x^4+5 x^5+\frac {6804}{25} x \log (3)-\frac {108}{5} x^2 \log (3)-68 x^3 \log (3)+20 x^4 \log (3)-\frac {594}{5} x \log ^2(3)-48 x^2 \log ^2(3)+30 x^3 \log ^2(3)+\frac {1}{5} (1+10 x)^2 \log ^3(3)-\frac {1}{125} x \left (21349-625 \log ^4(3)\right )\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.03, size = 105, normalized size = 5.53 \begin {gather*} -\frac {21349 x}{125}+\frac {2069 x^2}{25}+5 x^5+\frac {6804}{25} x \log (3)-\frac {108}{5} x^2 \log (3)-\frac {594}{5} x \log ^2(3)-48 x^2 \log ^2(3)+4 x \log ^3(3)+20 x^2 \log ^3(3)+5 x \log ^4(3)+2 x^4 (-13+10 \log (3))+\frac {2}{5} x^3 \left (63-170 \log (3)+75 \log ^2(3)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.06, size = 87, normalized size = 4.58 \begin {gather*} 5 \, x^{5} + 5 \, x \log \relax (3)^{4} - 26 \, x^{4} + 4 \, {\left (5 \, x^{2} + x\right )} \log \relax (3)^{3} + \frac {126}{5} \, x^{3} + \frac {6}{5} \, {\left (25 \, x^{3} - 40 \, x^{2} - 99 \, x\right )} \log \relax (3)^{2} + \frac {2069}{25} \, x^{2} + \frac {4}{25} \, {\left (125 \, x^{4} - 425 \, x^{3} - 135 \, x^{2} + 1701 \, x\right )} \log \relax (3) - \frac {21349}{125} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.15, size = 87, normalized size = 4.58 \begin {gather*} 5 \, x^{5} + 5 \, x \log \relax (3)^{4} - 26 \, x^{4} + 4 \, {\left (5 \, x^{2} + x\right )} \log \relax (3)^{3} + \frac {126}{5} \, x^{3} + \frac {6}{5} \, {\left (25 \, x^{3} - 40 \, x^{2} - 99 \, x\right )} \log \relax (3)^{2} + \frac {2069}{25} \, x^{2} + \frac {4}{25} \, {\left (125 \, x^{4} - 425 \, x^{3} - 135 \, x^{2} + 1701 \, x\right )} \log \relax (3) - \frac {21349}{125} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 81, normalized size = 4.26
method | result | size |
norman | \(\left (20 \ln \relax (3)-26\right ) x^{4}+\left (30 \ln \relax (3)^{2}-68 \ln \relax (3)+\frac {126}{5}\right ) x^{3}+\left (20 \ln \relax (3)^{3}-48 \ln \relax (3)^{2}-\frac {108 \ln \relax (3)}{5}+\frac {2069}{25}\right ) x^{2}+\left (5 \ln \relax (3)^{4}+4 \ln \relax (3)^{3}-\frac {594 \ln \relax (3)^{2}}{5}+\frac {6804 \ln \relax (3)}{25}-\frac {21349}{125}\right ) x +5 x^{5}\) | \(81\) |
gosper | \(\frac {x \left (625 \ln \relax (3)^{4}+2500 x \ln \relax (3)^{3}+3750 x^{2} \ln \relax (3)^{2}+2500 x^{3} \ln \relax (3)+625 x^{4}+500 \ln \relax (3)^{3}-6000 x \ln \relax (3)^{2}-8500 x^{2} \ln \relax (3)-3250 x^{3}-14850 \ln \relax (3)^{2}-2700 x \ln \relax (3)+3150 x^{2}+34020 \ln \relax (3)+10345 x -21349\right )}{125}\) | \(88\) |
default | \(5 x \ln \relax (3)^{4}+\frac {\ln \relax (3)^{3} \left (2500 x^{2}+500 x \right )}{125}+\frac {\ln \relax (3)^{2} \left (3750 x^{3}-6000 x^{2}-14850 x \right )}{125}+\frac {\ln \relax (3) \left (2500 x^{4}-8500 x^{3}-2700 x^{2}+34020 x \right )}{125}+5 x^{5}-26 x^{4}+\frac {126 x^{3}}{5}+\frac {2069 x^{2}}{25}-\frac {21349 x}{125}\) | \(90\) |
risch | \(5 x \ln \relax (3)^{4}+20 \ln \relax (3)^{3} x^{2}+4 x \ln \relax (3)^{3}+30 x^{3} \ln \relax (3)^{2}-48 x^{2} \ln \relax (3)^{2}-\frac {594 x \ln \relax (3)^{2}}{5}+20 x^{4} \ln \relax (3)-68 x^{3} \ln \relax (3)-\frac {108 x^{2} \ln \relax (3)}{5}+\frac {6804 x \ln \relax (3)}{25}+5 x^{5}-26 x^{4}+\frac {126 x^{3}}{5}+\frac {2069 x^{2}}{25}-\frac {21349 x}{125}\) | \(99\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 87, normalized size = 4.58 \begin {gather*} 5 \, x^{5} + 5 \, x \log \relax (3)^{4} - 26 \, x^{4} + 4 \, {\left (5 \, x^{2} + x\right )} \log \relax (3)^{3} + \frac {126}{5} \, x^{3} + \frac {6}{5} \, {\left (25 \, x^{3} - 40 \, x^{2} - 99 \, x\right )} \log \relax (3)^{2} + \frac {2069}{25} \, x^{2} + \frac {4}{25} \, {\left (125 \, x^{4} - 425 \, x^{3} - 135 \, x^{2} + 1701 \, x\right )} \log \relax (3) - \frac {21349}{125} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.19, size = 81, normalized size = 4.26 \begin {gather*} 5\,x^5+\left (20\,\ln \relax (3)-26\right )\,x^4+\left (30\,{\ln \relax (3)}^2-68\,\ln \relax (3)+\frac {126}{5}\right )\,x^3+\left (20\,{\ln \relax (3)}^3-48\,{\ln \relax (3)}^2-\frac {108\,\ln \relax (3)}{5}+\frac {2069}{25}\right )\,x^2+\left (\frac {6804\,\ln \relax (3)}{25}-\frac {594\,{\ln \relax (3)}^2}{5}+4\,{\ln \relax (3)}^3+5\,{\ln \relax (3)}^4-\frac {21349}{125}\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 94, normalized size = 4.95 \begin {gather*} 5 x^{5} + x^{4} \left (-26 + 20 \log {\relax (3 )}\right ) + x^{3} \left (- 68 \log {\relax (3 )} + \frac {126}{5} + 30 \log {\relax (3 )}^{2}\right ) + x^{2} \left (- 48 \log {\relax (3 )}^{2} - \frac {108 \log {\relax (3 )}}{5} + 20 \log {\relax (3 )}^{3} + \frac {2069}{25}\right ) + x \left (- \frac {21349}{125} - \frac {594 \log {\relax (3 )}^{2}}{5} + 4 \log {\relax (3 )}^{3} + 5 \log {\relax (3 )}^{4} + \frac {6804 \log {\relax (3 )}}{25}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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