Optimal. Leaf size=24 \[ \left (e^{e^3}+2 x-x^2+x^3 (1+\log (x))\right )^2 \]
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Rubi [B] time = 0.11, antiderivative size = 93, normalized size of antiderivative = 3.88, number of steps used = 10, number of rules used = 3, integrand size = 78, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {2356, 2304, 2305} \begin {gather*} x^6+x^6 \log ^2(x)+2 x^6 \log (x)-2 x^5-2 x^5 \log (x)+5 x^4+4 x^4 \log (x)+2 e^{e^3} x^3-4 x^3+2 e^{e^3} x^3 \log (x)-2 e^{e^3} x^2+4 x^2+4 e^{e^3} x \end {gather*}
Antiderivative was successfully verified.
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Rule 2304
Rule 2305
Rule 2356
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 x^2-4 x^3+6 x^4-\frac {12 x^5}{5}+\frac {4 x^6}{3}+6 \int x^5 \log ^2(x) \, dx+e^{e^3} \int \left (4-4 x+8 x^2\right ) \, dx+\int \left (6 e^{e^3} x^2+16 x^3-10 x^4+14 x^5\right ) \log (x) \, dx\\ &=4 e^{e^3} x+4 x^2-2 e^{e^3} x^2-4 x^3+\frac {8}{3} e^{e^3} x^3+6 x^4-\frac {12 x^5}{5}+\frac {4 x^6}{3}+x^6 \log ^2(x)-2 \int x^5 \log (x) \, dx+\int \left (6 e^{e^3} x^2 \log (x)+16 x^3 \log (x)-10 x^4 \log (x)+14 x^5 \log (x)\right ) \, dx\\ &=4 e^{e^3} x+4 x^2-2 e^{e^3} x^2-4 x^3+\frac {8}{3} e^{e^3} x^3+6 x^4-\frac {12 x^5}{5}+\frac {25 x^6}{18}-\frac {1}{3} x^6 \log (x)+x^6 \log ^2(x)-10 \int x^4 \log (x) \, dx+14 \int x^5 \log (x) \, dx+16 \int x^3 \log (x) \, dx+\left (6 e^{e^3}\right ) \int x^2 \log (x) \, dx\\ &=4 e^{e^3} x+4 x^2-2 e^{e^3} x^2-4 x^3+2 e^{e^3} x^3+5 x^4-2 x^5+x^6+2 e^{e^3} x^3 \log (x)+4 x^4 \log (x)-2 x^5 \log (x)+2 x^6 \log (x)+x^6 \log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 24, normalized size = 1.00 \begin {gather*} \left (e^{e^3}+x \left (2-x+x^2\right )+x^3 \log (x)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.53, size = 74, normalized size = 3.08 \begin {gather*} x^{6} \log \relax (x)^{2} + x^{6} - 2 \, x^{5} + 5 \, x^{4} - 4 \, x^{3} + 4 \, x^{2} + 2 \, {\left (x^{3} - x^{2} + 2 \, x\right )} e^{\left (e^{3}\right )} + 2 \, {\left (x^{6} - x^{5} + 2 \, x^{4} + x^{3} e^{\left (e^{3}\right )}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 90, normalized size = 3.75 \begin {gather*} x^{6} \log \relax (x)^{2} + 2 \, x^{6} \log \relax (x) + x^{6} - 2 \, x^{5} \log \relax (x) - 2 \, x^{5} + 4 \, x^{4} \log \relax (x) + 2 \, x^{3} e^{\left (e^{3}\right )} \log \relax (x) + 5 \, x^{4} - \frac {2}{3} \, x^{3} e^{\left (e^{3}\right )} - 4 \, x^{3} + 4 \, x^{2} + \frac {2}{3} \, {\left (4 \, x^{3} - 3 \, x^{2} + 6 \, x\right )} e^{\left (e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.07, size = 82, normalized size = 3.42
method | result | size |
norman | \(x^{6}+x^{6} \ln \relax (x )^{2}+\left (-2 \,{\mathrm e}^{{\mathrm e}^{3}}+4\right ) x^{2}+\left (2 \,{\mathrm e}^{{\mathrm e}^{3}}-4\right ) x^{3}+5 x^{4}-2 x^{5}+4 x \,{\mathrm e}^{{\mathrm e}^{3}}+4 x^{4} \ln \relax (x )-2 x^{5} \ln \relax (x )+2 x^{6} \ln \relax (x )+2 \,{\mathrm e}^{{\mathrm e}^{3}} \ln \relax (x ) x^{3}\) | \(82\) |
risch | \(x^{6} \ln \relax (x )^{2}+2 x^{6} \ln \relax (x )-2 x^{5} \ln \relax (x )+x^{6}+2 \,{\mathrm e}^{{\mathrm e}^{3}} \ln \relax (x ) x^{3}+4 x^{4} \ln \relax (x )-2 x^{5}+2 x^{3} {\mathrm e}^{{\mathrm e}^{3}}+5 x^{4}-2 x^{2} {\mathrm e}^{{\mathrm e}^{3}}-4 x^{3}+4 x \,{\mathrm e}^{{\mathrm e}^{3}}+4 x^{2}\) | \(86\) |
default | \(2 x^{6} \ln \relax (x )+x^{6}-2 x^{5} \ln \relax (x )-2 x^{5}+2 \,{\mathrm e}^{{\mathrm e}^{3}} \ln \relax (x ) x^{3}-\frac {2 x^{3} {\mathrm e}^{{\mathrm e}^{3}}}{3}+4 x^{4} \ln \relax (x )+5 x^{4}+{\mathrm e}^{{\mathrm e}^{3}} \left (\frac {8}{3} x^{3}-2 x^{2}+4 x \right )+4 x^{2}-4 x^{3}+x^{6} \ln \relax (x )^{2}\) | \(90\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.37, size = 98, normalized size = 4.08 \begin {gather*} \frac {1}{18} \, {\left (18 \, \log \relax (x)^{2} - 6 \, \log \relax (x) + 1\right )} x^{6} + \frac {17}{18} \, x^{6} - 2 \, x^{5} + 5 \, x^{4} - \frac {2}{3} \, x^{3} e^{\left (e^{3}\right )} - 4 \, x^{3} + 4 \, x^{2} + \frac {2}{3} \, {\left (4 \, x^{3} - 3 \, x^{2} + 6 \, x\right )} e^{\left (e^{3}\right )} + \frac {1}{3} \, {\left (7 \, x^{6} - 6 \, x^{5} + 12 \, x^{4} + 6 \, x^{3} e^{\left (e^{3}\right )}\right )} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.67, size = 39, normalized size = 1.62 \begin {gather*} x\,\left (x^2\,\ln \relax (x)-x+x^2+2\right )\,\left (2\,x+2\,{\mathrm {e}}^{{\mathrm {e}}^3}+x^3\,\ln \relax (x)-x^2+x^3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 82, normalized size = 3.42 \begin {gather*} x^{6} \log {\relax (x )}^{2} + x^{6} - 2 x^{5} + 5 x^{4} + x^{3} \left (-4 + 2 e^{e^{3}}\right ) + x^{2} \left (4 - 2 e^{e^{3}}\right ) + 4 x e^{e^{3}} + \left (2 x^{6} - 2 x^{5} + 4 x^{4} + 2 x^{3} e^{e^{3}}\right ) \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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