Optimal. Leaf size=39 \[ -\frac {3 x^4}{128}+\frac {1}{4} x^4 \log ^3(x)-\frac {3}{16} x^4 \log ^2(x)+\frac {3}{32} x^4 \log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2305, 2304} \[ -\frac {3 x^4}{128}+\frac {1}{4} x^4 \log ^3(x)-\frac {3}{16} x^4 \log ^2(x)+\frac {3}{32} x^4 \log (x) \]
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int x^3 \log ^3(x) \, dx &=\frac {1}{4} x^4 \log ^3(x)-\frac {3}{4} \int x^3 \log ^2(x) \, dx\\ &=-\frac {3}{16} x^4 \log ^2(x)+\frac {1}{4} x^4 \log ^3(x)+\frac {3}{8} \int x^3 \log (x) \, dx\\ &=-\frac {3 x^4}{128}+\frac {3}{32} x^4 \log (x)-\frac {3}{16} x^4 \log ^2(x)+\frac {1}{4} x^4 \log ^3(x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 39, normalized size = 1.00 \[ -\frac {3 x^4}{128}+\frac {1}{4} x^4 \log ^3(x)-\frac {3}{16} x^4 \log ^2(x)+\frac {3}{32} x^4 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 31, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} \log \relax (x)^{3} - \frac {3}{16} \, x^{4} \log \relax (x)^{2} + \frac {3}{32} \, x^{4} \log \relax (x) - \frac {3}{128} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 31, normalized size = 0.79 \[ \frac {1}{4} \, x^{4} \log \relax (x)^{3} - \frac {3}{16} \, x^{4} \log \relax (x)^{2} + \frac {3}{32} \, x^{4} \log \relax (x) - \frac {3}{128} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 32, normalized size = 0.82 \[ \frac {x^{4} \ln \relax (x )^{3}}{4}-\frac {3 x^{4} \ln \relax (x )^{2}}{16}+\frac {3 x^{4} \ln \relax (x )}{32}-\frac {3 x^{4}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 23, normalized size = 0.59 \[ \frac {1}{128} \, {\left (32 \, \log \relax (x)^{3} - 24 \, \log \relax (x)^{2} + 12 \, \log \relax (x) - 3\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 23, normalized size = 0.59 \[ \frac {3\,x^4\,\left (\frac {32\,{\ln \relax (x)}^3}{3}-8\,{\ln \relax (x)}^2+4\,\ln \relax (x)-1\right )}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 37, normalized size = 0.95 \[ \frac {x^{4} \log {\relax (x )}^{3}}{4} - \frac {3 x^{4} \log {\relax (x )}^{2}}{16} + \frac {3 x^{4} \log {\relax (x )}}{32} - \frac {3 x^{4}}{128} \]
Verification of antiderivative is not currently implemented for this CAS.
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