Optimal. Leaf size=39 \[ -\frac {3 x^4}{128}+\frac {3}{32} x^4 \log (x)-\frac {3}{16} x^4 \log ^2(x)+\frac {1}{4} x^4 \log ^3(x) \]
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Rubi [A]
time = 0.02, 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 = {2342, 2341}
\begin {gather*} -\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) \end {gather*}
Antiderivative was successfully verified.
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Rule 2341
Rule 2342
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 \begin {gather*} -\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 {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.74, size = 23, normalized size = 0.59 \begin {gather*} \frac {x^4 \left (-3-24 \text {Log}\left [x\right ]^2+12 \text {Log}\left [x\right ]+32 \text {Log}\left [x\right ]^3\right )}{128} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 32, normalized size = 0.82
method | result | size |
default | \(-\frac {3 x^{4}}{128}+\frac {3 x^{4} \ln \left (x \right )}{32}-\frac {3 x^{4} \ln \left (x \right )^{2}}{16}+\frac {x^{4} \ln \left (x \right )^{3}}{4}\) | \(32\) |
norman | \(-\frac {3 x^{4}}{128}+\frac {3 x^{4} \ln \left (x \right )}{32}-\frac {3 x^{4} \ln \left (x \right )^{2}}{16}+\frac {x^{4} \ln \left (x \right )^{3}}{4}\) | \(32\) |
risch | \(-\frac {3 x^{4}}{128}+\frac {3 x^{4} \ln \left (x \right )}{32}-\frac {3 x^{4} \ln \left (x \right )^{2}}{16}+\frac {x^{4} \ln \left (x \right )^{3}}{4}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 0.59 \begin {gather*} \frac {1}{128} \, {\left (32 \, \log \left (x\right )^{3} - 24 \, \log \left (x\right )^{2} + 12 \, \log \left (x\right ) - 3\right )} x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 31, normalized size = 0.79 \begin {gather*} \frac {1}{4} \, x^{4} \log \left (x\right )^{3} - \frac {3}{16} \, x^{4} \log \left (x\right )^{2} + \frac {3}{32} \, x^{4} \log \left (x\right ) - \frac {3}{128} \, x^{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 37, normalized size = 0.95 \begin {gather*} \frac {x^{4} \log {\left (x \right )}^{3}}{4} - \frac {3 x^{4} \log {\left (x \right )}^{2}}{16} + \frac {3 x^{4} \log {\left (x \right )}}{32} - \frac {3 x^{4}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 40, normalized size = 1.03 \begin {gather*} \frac {1}{4} x^{4} \ln ^{3}x-\frac {3}{16} x^{4} \ln ^{2}x-\frac {3}{128} x^{4}+\frac {3}{32} x^{4} \ln x \end {gather*}
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 \begin {gather*} \frac {3\,x^4\,\left (\frac {32\,{\ln \left (x\right )}^3}{3}-8\,{\ln \left (x\right )}^2+4\,\ln \left (x\right )-1\right )}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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