Optimal. Leaf size=9 \[ 62500 x^5 \log ^2(x) \]
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Rubi [A] time = 0.03, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {2304, 2305} \begin {gather*} 62500 x^5 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=125000 \int x^4 \log (x) \, dx+312500 \int x^4 \log ^2(x) \, dx\\ &=-5000 x^5+25000 x^5 \log (x)+62500 x^5 \log ^2(x)-125000 \int x^4 \log (x) \, dx\\ &=62500 x^5 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} 62500 x^5 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 9, normalized size = 1.00 \begin {gather*} 62500 \, x^{5} \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 1.00 \begin {gather*} 62500 \, x^{5} \log \relax (x)^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 1.11
method | result | size |
default | \(62500 x^{5} \ln \relax (x )^{2}\) | \(10\) |
norman | \(62500 x^{5} \ln \relax (x )^{2}\) | \(10\) |
risch | \(62500 x^{5} \ln \relax (x )^{2}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.34, size = 30, normalized size = 3.33 \begin {gather*} 2500 \, {\left (25 \, \log \relax (x)^{2} - 10 \, \log \relax (x) + 2\right )} x^{5} + 25000 \, x^{5} \log \relax (x) - 5000 \, x^{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.50, size = 9, normalized size = 1.00 \begin {gather*} 62500\,x^5\,{\ln \relax (x)}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.89 \begin {gather*} 62500 x^{5} \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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