Optimal. Leaf size=24 \[ \frac {x^4}{2}+4 x^4 \log ^2(x)-2 x^4 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 2305, 2304} \[ \frac {x^4}{2}+4 x^4 \log ^2(x)-2 x^4 \log (x) \]
Antiderivative was successfully verified.
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Rule 12
Rule 2304
Rule 2305
Rubi steps
\begin {align*} \int 16 x^3 \log ^2(x) \, dx &=16 \int x^3 \log ^2(x) \, dx\\ &=4 x^4 \log ^2(x)-8 \int x^3 \log (x) \, dx\\ &=\frac {x^4}{2}-2 x^4 \log (x)+4 x^4 \log ^2(x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.25 \[ 16 \left (\frac {x^4}{32}+\frac {1}{4} x^4 \log ^2(x)-\frac {1}{8} x^4 \log (x)\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 22, normalized size = 0.92 \[ 4 \, x^{4} \log \relax (x)^{2} - 2 \, x^{4} \log \relax (x) + \frac {1}{2} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 22, normalized size = 0.92 \[ 4 \, x^{4} \log \relax (x)^{2} - 2 \, x^{4} \log \relax (x) + \frac {1}{2} \, x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 23, normalized size = 0.96 \[ 4 x^{4} \ln \relax (x )^{2}-2 x^{4} \ln \relax (x )+\frac {x^{4}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 17, normalized size = 0.71 \[ \frac {1}{2} \, {\left (8 \, \log \relax (x)^{2} - 4 \, \log \relax (x) + 1\right )} x^{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 17, normalized size = 0.71 \[ \frac {x^4\,\left (8\,{\ln \relax (x)}^2-4\,\ln \relax (x)+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 22, normalized size = 0.92 \[ 4 x^{4} \log {\relax (x )}^{2} - 2 x^{4} \log {\relax (x )} + \frac {x^{4}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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