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 = 0.0303477, antiderivative size = 39, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, 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 2305
Rule 2304
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*}
Mathematica [A] time = 0.0012574, size = 39, normalized size = 1. \[ -\frac{3 x^4}{128}+\frac{1}{4} x^4 \log ^3(x)-\frac{3}{16} x^4 \log ^2(x)+\frac{3}{32} x^4 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 32, normalized size = 0.8 \begin{align*} -{\frac{3\,{x}^{4}}{128}}+{\frac{3\,{x}^{4}\ln \left ( x \right ) }{32}}-{\frac{3\,{x}^{4} \left ( \ln \left ( x \right ) \right ) ^{2}}{16}}+{\frac{{x}^{4} \left ( \ln \left ( x \right ) \right ) ^{3}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926354, size = 31, normalized size = 0.79 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.501457, size = 92, normalized size = 2.36 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.125523, size = 37, normalized size = 0.95 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10217, size = 42, normalized size = 1.08 \begin{align*} \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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