Optimal. Leaf size=21 \[ x-x^2+5376 x \left (x-x^2 \log ^2(x)\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 16, normalized size of antiderivative = 0.76, number of steps used = 4, number of rules used = 2, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2304, 2305} \begin {gather*} -5376 x^3 \log ^2(x)+5375 x^2+x \end {gather*}
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+5375 x^2-10752 \int x^2 \log (x) \, dx-16128 \int x^2 \log ^2(x) \, dx\\ &=x+5375 x^2+\frac {3584 x^3}{3}-3584 x^3 \log (x)-5376 x^3 \log ^2(x)+10752 \int x^2 \log (x) \, dx\\ &=x+5375 x^2-5376 x^3 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.76 \begin {gather*} x+5375 x^2-5376 x^3 \log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 16, normalized size = 0.76 \begin {gather*} -5376 \, x^{3} \log \relax (x)^{2} + 5375 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 16, normalized size = 0.76 \begin {gather*} -5376 \, x^{3} \log \relax (x)^{2} + 5375 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 17, normalized size = 0.81
method | result | size |
default | \(5375 x^{2}+x -5376 x^{3} \ln \relax (x )^{2}\) | \(17\) |
norman | \(5375 x^{2}+x -5376 x^{3} \ln \relax (x )^{2}\) | \(17\) |
risch | \(5375 x^{2}+x -5376 x^{3} \ln \relax (x )^{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 36, normalized size = 1.71 \begin {gather*} -\frac {1792}{3} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} - 3584 \, x^{3} \log \relax (x) + \frac {3584}{3} \, x^{3} + 5375 \, x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.09, size = 16, normalized size = 0.76 \begin {gather*} -5376\,x^3\,{\ln \relax (x)}^2+5375\,x^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.71 \begin {gather*} - 5376 x^{3} \log {\relax (x )}^{2} + 5375 x^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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