Optimal. Leaf size=22 \[ \frac {16}{625} \left (2+\frac {4}{3} x^3 (3-x+\log (x))^2\right ) \]
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Rubi [B] time = 0.07, antiderivative size = 59, normalized size of antiderivative = 2.68, number of steps used = 9, number of rules used = 6, integrand size = 43, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.140, Rules used = {12, 1593, 43, 2334, 2305, 2304} \begin {gather*} \frac {64 x^5}{1875}-\frac {128 x^4}{625}+\frac {192 x^3}{625}+\frac {64 x^3 \log ^2(x)}{1875}-\frac {128 x^3 \log (x)}{5625}+\frac {128 \left (10 x^3-3 x^4\right ) \log (x)}{5625} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 43
Rule 1593
Rule 2304
Rule 2305
Rule 2334
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (2112 x^2-1664 x^3+320 x^4+\left (1280 x^2-512 x^3\right ) \log (x)+192 x^2 \log ^2(x)\right ) \, dx}{1875}\\ &=\frac {704 x^3}{1875}-\frac {416 x^4}{1875}+\frac {64 x^5}{1875}+\frac {\int \left (1280 x^2-512 x^3\right ) \log (x) \, dx}{1875}+\frac {64}{625} \int x^2 \log ^2(x) \, dx\\ &=\frac {704 x^3}{1875}-\frac {416 x^4}{1875}+\frac {64 x^5}{1875}+\frac {64 x^3 \log ^2(x)}{1875}+\frac {\int (1280-512 x) x^2 \log (x) \, dx}{1875}-\frac {128 \int x^2 \log (x) \, dx}{1875}\\ &=\frac {6464 x^3}{16875}-\frac {416 x^4}{1875}+\frac {64 x^5}{1875}-\frac {128 x^3 \log (x)}{5625}+\frac {128 \left (10 x^3-3 x^4\right ) \log (x)}{5625}+\frac {64 x^3 \log ^2(x)}{1875}-\frac {\int \frac {128}{3} (10-3 x) x^2 \, dx}{1875}\\ &=\frac {6464 x^3}{16875}-\frac {416 x^4}{1875}+\frac {64 x^5}{1875}-\frac {128 x^3 \log (x)}{5625}+\frac {128 \left (10 x^3-3 x^4\right ) \log (x)}{5625}+\frac {64 x^3 \log ^2(x)}{1875}-\frac {128 \int (10-3 x) x^2 \, dx}{5625}\\ &=\frac {6464 x^3}{16875}-\frac {416 x^4}{1875}+\frac {64 x^5}{1875}-\frac {128 x^3 \log (x)}{5625}+\frac {128 \left (10 x^3-3 x^4\right ) \log (x)}{5625}+\frac {64 x^3 \log ^2(x)}{1875}-\frac {128 \int \left (10 x^2-3 x^3\right ) \, dx}{5625}\\ &=\frac {192 x^3}{625}-\frac {128 x^4}{625}+\frac {64 x^5}{1875}-\frac {128 x^3 \log (x)}{5625}+\frac {128 \left (10 x^3-3 x^4\right ) \log (x)}{5625}+\frac {64 x^3 \log ^2(x)}{1875}\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.01, size = 51, normalized size = 2.32 \begin {gather*} \frac {192 x^3}{625}-\frac {128 x^4}{625}+\frac {64 x^5}{1875}+\frac {128}{625} x^3 \log (x)-\frac {128 x^4 \log (x)}{1875}+\frac {64 x^3 \log ^2(x)}{1875} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.26, size = 38, normalized size = 1.73 \begin {gather*} \frac {64}{1875} \, x^{5} + \frac {64}{1875} \, x^{3} \log \relax (x)^{2} - \frac {128}{625} \, x^{4} + \frac {192}{625} \, x^{3} - \frac {128}{1875} \, {\left (x^{4} - 3 \, x^{3}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.42, size = 39, normalized size = 1.77 \begin {gather*} \frac {64}{1875} \, x^{5} - \frac {128}{1875} \, x^{4} \log \relax (x) + \frac {64}{1875} \, x^{3} \log \relax (x)^{2} - \frac {128}{625} \, x^{4} + \frac {128}{625} \, x^{3} \log \relax (x) + \frac {192}{625} \, x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 40, normalized size = 1.82
method | result | size |
default | \(\frac {192 x^{3}}{625}-\frac {128 x^{4}}{625}+\frac {64 x^{5}}{1875}+\frac {64 x^{3} \ln \relax (x )^{2}}{1875}+\frac {128 x^{3} \ln \relax (x )}{625}-\frac {128 x^{4} \ln \relax (x )}{1875}\) | \(40\) |
norman | \(\frac {192 x^{3}}{625}-\frac {128 x^{4}}{625}+\frac {64 x^{5}}{1875}+\frac {64 x^{3} \ln \relax (x )^{2}}{1875}+\frac {128 x^{3} \ln \relax (x )}{625}-\frac {128 x^{4} \ln \relax (x )}{1875}\) | \(40\) |
risch | \(\frac {192 x^{3}}{625}-\frac {128 x^{4}}{625}+\frac {64 x^{5}}{1875}+\frac {64 x^{3} \ln \relax (x )^{2}}{1875}+\frac {128 x^{3} \ln \relax (x )}{625}-\frac {128 x^{4} \ln \relax (x )}{1875}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.38, size = 48, normalized size = 2.18 \begin {gather*} \frac {64}{1875} \, x^{5} + \frac {64}{16875} \, {\left (9 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 2\right )} x^{3} - \frac {128}{625} \, x^{4} + \frac {5056}{16875} \, x^{3} - \frac {128}{5625} \, {\left (3 \, x^{4} - 10 \, x^{3}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.76, size = 14, normalized size = 0.64 \begin {gather*} \frac {64\,x^3\,{\left (\ln \relax (x)-x+3\right )}^2}{1875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.14, size = 48, normalized size = 2.18 \begin {gather*} \frac {64 x^{5}}{1875} - \frac {128 x^{4}}{625} + \frac {64 x^{3} \log {\relax (x )}^{2}}{1875} + \frac {192 x^{3}}{625} + \left (- \frac {128 x^{4}}{1875} + \frac {128 x^{3}}{625}\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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